I've driven in both Phuket (scooter) and Langkawi (car) and there is a bit of difference (obviously) in the traffic. Driving in Langkawi is a breeze, not a lot of traffic.

Driving in Phuket is not at all impossible, but it will be a lot more packed (especially in/around Patong). And the intersections can be... interesting

As long as you drive with care and don't get "pressured" by all the drivers honking their horn (a lot of them do it just to say: I am here, watch out) you should be perfectly fine.