u/noshowtho If you understand how a phased array can steer its output, then you are well on your way.

With a dish setup, all the energy for "pings" originates from a relatively concentrated point (which sometimes IS a small phased array) sitting at the focal point of the dish. You probably know that this is why dish systems have some sort of tripod or mechanical arm sitting out front, to hold the transmitter at that point. The transmitter "lights up" the dish, and the dish in turn focuses the emitted energy into a beam (with a major lobe). It's just like a flashlight, where the bulb throws off energy that is reflected and focused by the reflector behind it. Just like a flashlight, a dish antenna is aimed at targets by physically moving the dish around, although these days most dishes have a limited ability to do digital steering.

When the return signal (energy reflected off the target) comes back, the dish, being large, captures some of that energy and focuses it back on the focal point, onto a receiver sitting there. So the job of the dish is to take very low level energy arriving across a relatively large area and focus it down onto a specific point where the sensor sits. At this point it's operating a little like a telescope.

Unlike dish systems that transmit and receive energy from a concentrated point, phased arrays spread the transmit power out over many transmit modules arranged across a flat array. In the dish, the total power level out is the power of the one transmitter. In a phased array, the power out is the sum of the power of all the transmit modules.

For transmit, the phased array mimics the function of a dish by controlling the timing (phase) of the energy leaving each transmit module. This opens up all sorts of possibilities for creating different sorts of "pings" and avoids a lot of mechanical steering, as the array can be aimed digitally by controlling the energy coming from transmit modules individually.

Finally to your question. The return signal coming back to that flat phased array surface is again low level and spread across the entire array surface. But now, instead of a dish "multiplying" the intensity by focusing the energy like a telescope, the phased array simply sums the energy received at each receive module across the array surface. And since the returning wave front is captured at many point across the array, the post processing options are many times greater than that of a dish system.

The "better than" part of your question is significant. Better depends on what one is doing with the antenna system in the first place. Dish systems are relatively cheap, can be relatively simple, and depending on the scenario can outperform even really good phased arrays. But the electronic beam steering, beam forming capabilities, and post processing options for phased arrays make their expense and complexity worth it for many applications.