OK- The ATM 63 is a discontinued hypercardioid dynamic mic intended as a live instrument mic. It excels on guitar cabs and snare drum in particular, sort of Audio-Technica's spin on the SM57.
The AKG D310 is a cardioid stage mic with an internal pop filter intended as a stage vocal mic. Although I don't use it, I have extensive experience with the D320, which is a hypercardioid mic in the same series. Given it's neodymium magnet and hypercardioid polar pattern, I expect the AT mic has higher output, and better gain before feedback. It is also quite likely less forgiving and picky about positioning, as well as having a more aggressive and abrupt proximity field. In other words, when you get real close to it, the bass output goes way up, and it happens real fast.
My opinion- as a live vocal mic, I would prefer the D310, especially if you are not an expert with mics. It is, however, more prone to feedback, so if I was playing with a loud band in a room with parallel hard walls, and feedback was a problem, I might use the AT mic, find the distance from it that sounds good, and *don't move*. In your case, I'd say-use the D310 and never look back. Put the AT on something that doesn't move, like a guitar cab. Good luck-Richie
