Both bikes have their advantages and disadvantages. Depending on what you're doing at the time of course. For general biking, I'd recommend using the Mach bike because of its speed... that seriously helps get through the game well. The Acro bike is more for fun, doing tricks and all that. Getting across those bridgings is a nice factor for having the Acro Bike.
So... just choose the one you like better, speed or tricks pretty much. Don't expect to be doing too many special tricks on the Acro Bike though. ;D