Screw that, get a 270 wheel. The 360 games are at least playable with a spinner, while the 270 games suck suck suck with a 360 wheel.
But the real REAL REAL reason to use a 270 wheel is for all the new games. Crazy Taxi, Colin McRae, Need for Speed, Grand Prix Legends, Nascar 2003, blah blah blah.
If there is one genre of NEW arcade games that still lends itself to our little homemade cabinets it's....well, fighting games. But if there're two genres they are fighting games and racing games. And the new racing games are just so much fun with a wheel. I'd play crazy taxi with a wheel any day of the week and twice on sunday over paper boy. Grand Prix Legends v. Pole Position? No question. Super Offroad v. Colin McRae Rally 3? Common.
Get the 270 wheel and just use your spinner for the other games. Or don't.