For me, it is a combination of the two. Driving a car that is docile, manageable, reliable, and easy to live with on a daily basis includes my daily driver Nissan. While it is streetable, to me, that is not something that is really fun to just take out for cruising.
I merely want to make my Mustang a high powered car which has a manageable and reliable drivetrain that brings me great enjoyment when driving.
Then you want streetability AND fun. You can have them both in the same car, but one does not imply the presence of the other.