I'd say your best bet is to weigh your options based on what games you would most likely be playing.
This is obviously the most sound advice in the general sense.
For what it's worth, I built my control panel with both a 2nd player and a trackball. After 7 months of heavy use of my cabinet, if I absolutely *had* to pick one or the other to eliminate, it would be a tough choice but I think I'd ditch the 2nd player.
Some points to provide some context for my personal choice:
- fighting games (Street Fighter 2, etc.) have made up probably less than 1% of the gaming time on my cabinet (I actually thought I'd get a fair amount of play out of such titles, but real world experience has proven that fighters are not very important to me or my guests)
- most of my friends are pretty much non-gamers, so I like to have a collection of "pick up and play" party-type games. The trackball makes lots of these possible (Golden Tee, Shuffleshot, Shuuz, Bowling), and they're always a hit (even with my parents!)
- you can still have a throw down with a smack-talking buddy on classic titles (Pac-Man, Galaga, Burgertime, Frogger, etc.) because the two players take turns using the one joystick (in fact, I'd estimate that upwards of 75% of the 2-player gaming I do on my cabinet falls into this category)
- I've found that I enjoy the "golden era" type titles (such as the ones mentioned in the previous point) more than the late 80's / early 90's titles which often included multiplayer simultaneous play (Ninja Turtles, Final Fight, X-Men, etc.) If you have a strong preference for these latter titles and ones like them, you will probably really miss the 2nd joystick. Personally, while I loved these games back in the day, I find they're just not the same on a home cabinet with a bottomless pit of virtual quarters in your pocket because there are no stakes
- This might be a controversial point to purists, but the trackball at least provides you a means of analog control. Why does this matter? Well, you'll quickly learn why if you try to play games like Star Wars, Pole Position, Hang On, and Major Havoc with an 8-way joystick. If you're willing to overlook the lack of authenticity in the controller design, you can actually play these games and believe it or not, they're still fun
- personally, I just flat out think the trackball is one of the coolest controller types ever. The precision it requires of you can really take the gaming experience up a notch and provide a nice change of pace from the billions of joystick games. The classic games that natively use a TB, IMO, can be great fun to practice and work on your scores (Missile Command, Centipede, Crystal Castles, Reactor, etc., etc.)
EDIT: one more thing. Again, the purists will cringe (heck, I'm cringing a bit) but one thing you could do is go with a trackball and outfit your cabinet with USB ports so that you can at least use a gamepad to play the simultaneous multi-player games when the need arises.