Just finished Shadow of the Beast on my Minimig, a little board this Dutch (I think) guy designed quite some time ago, that is basically a small board acting pretty much exactly as a real Amiga, only using an SD card instead of a floppy drive.
It uses real (9 pin) Amiga joysticks though.
There are some compatibility issues with certain games, but only a few... the vast majority work perfectly.
Anyway, the cool thing about the Minimig is that you hook it up directly to a TV, using a VGA cable... so it's a really convenient way to play Amiga games on TVs, and hooked up to a stereo as well (I'm getting really nice sound, using a very nice sound setup here).
One thing I like about the Minimig is that, just as on a real Amiga, you can't use savestates... using those can be so damn tempting at times, especially in difficult games such as Shadow of the Beast.
So in that way I'm glad it doesn't offer me the option, though it would have been convenient for other things though.