Environmental engineer here (part of which is hydrology).

I'm not at all an expert in American hydrology, but I can sketch a European situation.

In European droughts it is typically not at all effective that a drought-struck area receives a lot of rain (think of a typical summer intensive rain event). The soil will not be open for it, and therefore all the rain that will fall will directly run-off into rivers and canals and be removed from the area. That summer rain might seem like an awful lot of water, but the water balance of the area will not benefit from it at all.

Much more effective is an input of water on a longer term. That can be typically one of two things:

1. Longer rain events, like drizzle and light rain over the course of week(s). This will moisten the soil, after which it will be much more open to saturate the soil and groundwater supplies with the rain.
2. A source of water coming from upstream. This is mainly an effect for irrigated (dry) areas. If there is a well-developed irrigation network, steady input of upstream water will make it very resilient to local droughts. Catalonia (and northeast Spain in general) is a prime example of that. A region that is climatologically dry, but is fed huge amounts of water by irrigation from the Pyrenees, therefore sustaining a lot of agriculture.

Another alternative is to have preventive storage. This concerns filling up lakes and reservoirs when it's wet, so water can be released when there's a drought. This is for example how northern Italy ensures they have a constant supply of water, while in the meantime also using the stored water for creating energy through hydropower.

I don't know California, but perhaps you or other more US-specialized Redditors might be able to draw conclusions from this argumentation.

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So from what I've learned (not a professional just a curious person) it's better to feed the source because a drought affected area given a sudden burst of water will flood instantly. The ground is too dry to properly flow the water so it just sits on top which is typically what causes a flash flood. So feeding it to the source would allow it to actually distribute the water at an even pace without causing a sudden flood

Important to whom?

For plants and animals local precipitation is generally the most critical aspect, as they generally aren't tapping into underground water resources. On the other hand, they have been evolving to live in this area for a long, long time and over the last couple thousand years it looks like droughts lasting 10-20 years are pretty common, at least 2-4 decade long droughts hit during most centuries as far back as we seem to be able to tell from tree rings. Many plants basically stop the majority of their metabolic functions and try to wait out the dry periods, or they litter the desert with seeds that can hang around until conditions improve. Animal populations drop down to whatever level they can sustain and they shift themselves around into whatever micro climates they can hang on in, living for example in narrow canyons and nearer to whatever seasonal streams still exist and extracting the minimal water they need from the plant tissues they eat.

For human civilization and industrial uses local rainfall in the desert is actually more of a nuisance than a benefit. We already knew the rainfall was spotty and unreliable a hundred years ago so we've built our entire infrastructure around tapping the river and to a much smaller extent the underground water tables. As far as the entire Colorado River region cares the only thing that matters is the amount of snowpack on the west Rockies. Rain up there is not quite as helpful, but we just hold it behind the upstream dams. If the dams were full then upstream rain becomes relatively more problematic compared to the slow melt of good snowy conditions in the mountains.

California’s biggest agriculture area is mostly fed by the Sierra mountains snowpack. Warm winters where the snowpack doesn’t build up are worse for the water situation that cold winters.

Part of what made California’s agriculture so successful was that you could control how your crops got water, rather than relying on the weather to provide rain. With reservoirs silted up, dams beyond their planned limits, and consistently warmer winters the water situation isn’t as robust as it was and I can’t see it getting any better.

Edit - source is only that I lived there, no professional expertise.

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For CA ag we absolutely depend on the storage and planned release of winter snowpack; balanced to also provide flood protection from those same reservoirs. LA sucks from both sides of the Rockies and both sides of the Sierra, so there is that! (too many people in too dry an area). That said, "drought" is a human concept related to ag and city water supply. Extended lack of precip absolutely hurts local animal and plant (including fish) communities. Our attempts to engineer out of extended drought and climate change are very dicey (probably less snow, MAYBE less total precip) . The tunnels project and Delta pumping are an expensive, highly-contested mess. Conservation and less-water crops and desal are likely the eventual solutions in CA. IMHO. The "which is more important" answer is it depends where you live.

The answer to your question totally depends where you are and whether you're talking about agriculture or nature. In either case, plants care about moisture present in the soil vs moisture loss through transpiration. This is an American perspective, by the way.

Let's talk agriculture first. In some places, agriculture is rain-fed, for example the eastern US west of approximately the hundredth meridian (e.g., central Nebraska) and also the Pacific coast west of the Cascades and Sierra Nevada. In those places, rivers flowing by don't have much effect on soil moisture except at low elevations near the river--it's all about rain falling on the plants themselves. It is worth mentioning that in a lot of places, impermeable soil means that the ground can only soak up so much rain at a time. So if you get 3 inches of rain in, say, Virginia, you might store 1 inch in the soil and have 2 inches run off into streams, where it's not useful to farms (but may be useful--or harmful--to aquatic life downstream). This totally depends on the soil; sandy soils will soak up water whereas clay soils tend to be especially impermeable, and of course bedrock, rooftops, and paved surfaces don't absorb water. Counterintuitively, soil can be more impermeable when dry, so a heavy rain after a long drought may mean lots of runoff and not much water infiltration.

Natural plants are similar to rain-fed agriculture in that water in streams is not so useful to them, except in the riparian zone.

In other places (the dry western US), modern agriculture requires irrigation. Irrigation can come from rivers, renewable aquifers, or fossil aquifers (e.g., the Ogallala). For river irrigation, the Colorado river needs to be mentioned on its own because of the huge amount of land it irrigates and the huge amount of storage it has. In the Colorado river basin, most of the precipitation falls in mountains near the system's headwaters in Colorado and Wyoming, runs off and is stored in reservoirs, mainly in Lake Powell and Lake Mead (which have enough capacity to store a couple years of river flow), and is distributed to farms in dry places that would not support agriculture otherwise (e.g., California's Imperial Valley), plus lawns, golf courses, etc. Very little is allowed to reach the Gulf of California, a practice that devastated a formerly thriving ecosystem at the Colorado Delta. When we talk about drought on the Colorado river, we mean that less precipitation is falling than usual, meaning that reservoirs are low and still falling. Recovery from drought would mean more precipitation falling near the headwaters; agriculture in the Colorado basin is all about irrigation; given adequate irrigation, the dry climate for the farms can actually be a benefit (more sun, so more productive). Given the hole we are now in and the poor prospects for precipitation to increase in the future, we are probably going to have to adjust our expectations for how much water can actually be drawn from the river.

Other western river systems have parallels to the Colorado but are less extreme. In Idaho's Snake River Plain, for example, agriculture is mainly irrigated by the Snake River, tributaries to the Snake like the Boise and Payette, and renewable groundwater. All of these are mainly fed by snowmelt from the mountains. The region does get some snow and rain through the spring, and that does add moisture to the soil and help delay and reduce irrigation needs; however, it's just a fact of life in the area that the soil dries every single summer and you can't grow crops in the dry season without irrigation water. Reservoir storage (including year-to-year carryover) is significant, but smaller than on the Colorado (less than one year's worth of flow can be stored); the ability to benefit from water stored into the summer as seasonal snow is essential. In this area, recovery from drought mainly means lots of snow.

For fossil aquifers, like the Ogallala on the Great Plains, the aquifer will not be replenished on human timescales, so we should think of it just like we think of a mine: sustainable use is impossible, and once used up it's gone. In dry years, more irrigation water is needed, but the concept of drought does not apply to the aquifer itself.

Thank you for the informative reply!

.."...distributed to farms in dry places that would not support agriculture
otherwise (e.g., California's Imperial Valley), plus lawns, golf
courses, etc. Very little is allowed to reach the Gulf of California, a
practice that devastated a formerly thriving ecosystem at the Colorado
Delta.?"

Can I just say how much I hate lawns and golf courses!

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Yes. The ELI5 is that water runs along the surface of the ground a hecka lot faster than it soaks into it, especially in areas that are good for growing crops, which typically have clay within several feet of the surface. Clay is almost like a rubber to water, it moves very slowly through clay, about 1/4" per hour is absorbed. Unless you are in a major flooding event that lasts weeks, clays just don't absorb water fast enough to replenish the water table, you need that weekly soaking to get there.