Good news! I was able to get both games into my basement without too much hassle! The control panels on both machines are flush with the sides of the cabinets.
I tried X-Men vs. Street Fighter for just a couple of fights, and the controls seemed to work fine (except that Player 1 takes hardly any damage from each hit - I'm assuming this is in the settings somewhere). Also, its pretty loud, so I'm gonna have to find a volume control first thing. (No manual came with this game, and I'm completely new to owning a cabinet, so I'll have to do a little research). This is in a Konami (OOPS - I meant CAPCOM!) cabinet.
Tekken 2 came with a manual, and I noticed that the side of the machine says "Martial Champion", so that must be the game it was originally. I didn't have time to try that yet, but my buddies were playing it for a bit, and no one complained of any of the controls not working.
The games are missing locks and keys on the front, and the power panel on the back of X-Men hangs down inside the machine. Unless my power cord is plugged in - that holds it up. I don't see a power switch on Tekken 2. Is it safe to just unplug the games while they're running?
I'm pretty excited to start tinkering with these!