The comments suggest that Sony does not have the right controller for driving games.
I think the motion sensing for steering is awesome. I am surprised at how few use it. The downside is the lack of fine control of say an elongated stick or a wheel.
Ditto for the analog triggers for throttle and brakes - I think they are great.
By that point though, there are no convenient buttons for shifting gears. R1 and L1 are not optimal as user will primarily use their index fingers for the throttle and brakes. I considered the middle finger for the throttle and index finger for R1/L1 but thought it too busy. Ideally they could add buttons on the inside of the left and right stalk/grip accessible by the middle or third finger (call them L4/R4).
X/[] or X/O requires too much thumb travel.
As it is, my less-than-optimal solution is to use the X and the DPAD down arrow. There is no thumb travel as you use both thumbs and they are somewhat symmetric. As a further, bug counter-intuitive change, I use shift-up on the opposite side (down arrow). That allows me to balance activity between my two hands. One is operating the throttle and while one is shifting up and the opposite is true for braking and downshifting. There is an unanticipated downside - don't get an itch 'cause you never have a free hand.