Depends entirely on the particular virus or bacterium. Some are handled well by the immune system, some are not.

I think the real difference here is the availability/relevance of antibiotics vs. antivirals for treating certain symptoms. There are some situations where you can use antiviral drugs, but in many cases it isn't considered worth it (or there simply isn't an effective drug available). But we're also coming around to the fact that antibiotics probably should not be prescribed as often/freely as they have been historically.