I have never seen a side by side comparison of these 2 radios. However, that being said, there's one issue that many folks have run into with the R71. The operating system on this radio is kept on an EEPROM - meaning without battery backup, it can get erased.
Guess what? After all these years, that's exactly what is happening in many cases. There is, I believe, still one organization that sells replacement boards (that don't use an EEPROM to store the operating system), One individual I know who has installed an older version of these boards told me that it isn't a trivial matter.
I have never heard of that happening on the FRG100, although given its age, it certainly is a possibility. On the flip side, the R71 would be the clear winner in terms of selectivity (if the bandpass tuning is available - on later models, it wasn't, then it was brought back). The audio on the 100 would be better (to my ear, the R71 is muffled - I've played with a couple of them, and really didn't like it).
We have some links for receiver reviews in our wiki - I heartily recommend reading them and educating yourself. They can be found amongst the links in our receiver reviews category here...
Category:Receiver Reviews - The RadioReference Wiki
It also depends on what you want to hear with it - the R71 (with the ROM board
) would be an excellent receiver for hams and utilities - the FRG100 would have an edge if you were using it for casual listening and SW broadcasters. Of course if either receiver had any additional accessories, they would cost more.
I would also say your price range is just a little low - looking at the Universal Radio used list, I see a couple of R71s and a FRG100 for around USD460- but at that price, you could nab an used R75 (which is a real workhorse for many folks around here). You'd be wise to save up some cash