In the brief beta test I didn't get around to a lot of detailed customisation (it may have been somewhat locked), but if you stick to the default spec types that we had available...
Full Stock... is discouraged in game for not being competitive (no NOS)
Street... is encouraged for most races, has high grip, high top speed, not suitable for drifting unless you chuck the car into a tight corner, perform a scandinavian flick, or do donights from standstill.
Dirt... allows better drifts, but has a lower top speed which is bad for highways, fast roads, keeping up with friends, etc. My Dirt spec Camaro was a lower performance level than my Street one however, unlocking more upgrades could make it faster.
Now, it may just be that in the full game, with more time and career progression, you can make dirt spec cars faster, or you can completely customise by part, and essentially put 'dirt' tyres onto your street spec car, and voila, you can drift and enjoy the handling as we all hoped.
What do you guys think?
One of my videos - starting with Street spec, then switching to Dirt spec near the end