My experience is somewhere between the no-no and yes-yes camps.
I used my 060 A1200 for MP3 files for ages, and was happy with the sound. This was using Amplifier or AmigaAmp, via AHI's best quality Paula chip modes.
It was not as good as I'm now getting via Windows XP and a sound card, but it was pretty reasonable. The treble end of the spectrum was probably the most affected - I suspect the frequency response rolled off quite steeply after (guessing) 10Khz. I didn't try running it with doublePAL screen modes though, just scan doubled PAL. Apparently, this can affect the performance.
Mpeg was not as good. I tried Frogger and a few others, but it always seemed to me that the frame rate was a bit slow. Nonetheless, for some movies this was okay ;-)
Sound was patchy, probably due to the need to line up with the frame rate.
As far as I know, a towered A1200 (mine is a desktop), with a graphics card, can handle mpegs okay. I was stuck with AGA, which is notoriously slow at this kind of stuff.
Regards
David