Consider the case where you use a pencil to draw a coastline. The finest detail of the coastline that you can put down would be the size of the pencils tip, right? The comparison is not exact, but the principle is the same for radar and sonar.
There are many aspects that would characterize a radar system, I'd say that for the purpose of your question the receiver and frequency in this case might answer it for you.
The frequency of the sent signal does indeed reflect differently for differently sized objects, and this is why we can't observe some objects with radars. If they're small enough their radar cross section is below what the receiver would require or they are simply too transparent at the frequency we're operating at.
The receiver puts other limitations on the systems, with, as you've mentioned in your post, the lowest distinguishable power. The noise floor in a receiver is highly dependent on the type of amplifiers used and the antenna. Narrow beams pick up less RFI for example. With a lower noise floor, weaker signals can be detected, which means that for a fixed range, objects with a smaller radar cross section may be observed. Keep in mind however, that radar cross section is not the same as physical cross section, but is the term used when dealing with radars.