To understand PAL vs NTSC, you need to know a bit about the 2 TV formats. NTSC is an older TV standard and is not that great. It has hue issues, which is what made many dub NTSC as meaning Not The Same Color twice. It is basically not good at colour reproduction. PAL in contract is much better at colour reproduction. Apart from the colour differences. NTSC is a lower resolution than PAL. PAL contains 625 lines of usable resolution, whereas NTSC only 525 lines. So PAL has the advantage of 100 extra vertical lines of resolution. However NTSC has a faster refresh rate than PAL. The reason for this is the power supply used in the 2 regions. In the US they use electrical power at 60 herta, so for technical reasons the NTSC signal was sent out at 60 fields per second (or 60Hz). In contrast, in PAL regions the electrical supply uses 50 hertz, so the PAL broadcast signals were sent out at 50 fields per second (or 50Hz).

So:
NTSC = 525 lines at 30 frames per second (60Hz interlaced)
PAL = 625 lines at 25 frames per second (50Hz interlaced)

This all means that PAL Amigas have a higher TV screen resolution but run at 25 FPS and NTSC Amigas have a lower TV screen solution but run at 30FPS.

This explains the reason why games will run faster on an NTSC Amiga than they will on a PAL Amiga. The NTSC Amiga is running them 5FPS faster, which is great for something like Beat 'em ups or shooting games.

In answer to compatibility, a PAL Amiga is more compatible than an NTSC one, purely because a lot of games were developed in the UK for the PAL market. When a PAL Amiga runs a game originally developed for the US NTSC market it will run the game in the upper part of the screen with a black 100 pixel high blank area at the bottom of the screen. Quite a few commercial games in Europe ran like this on the Amiga because they were directly imported from the US versions and being lasy the developers never bothered to stretch the screen to fit. They will obviously be running slower on a PAL Amiga than they would on an NTSC Amiga because of the slower screen refresh rate and therefore FPS. You can switch a PAL A1200 into NTSC mode to pull an NTSC game or other program down into an NTSC screen, so that is a work around, and this will speed up the refresh rate to NTSC speeds. But you need a compatible TV or monitor for this to work.

And as you have found, NTSC Amigas are not as compatible. Trying to run PAL software on an NTSC Amiga will cause issues because it hasn't got the vertical screen resolution so will chop off the bottom of the screen, or the software just wont like it and cause glitches or crash.

Personally I would go with a PAL A1200, but I'm bias being in the UK. I'm not sure what US Amiga users would prefer to own but it would be interesting to know.

I hope that helps.