Be careful here. There are minor differences between the Heer and Waffen SS Panzer clothing. The SS style has rounder lapels, not as pointed as the Heer clothing, and the SS jacket also lacks the prominent centre seam down the back. It also had a straight cut front flap, differing from the tapering style used by the Heer. Having said that, some SS crews were issued with Heer clothing early in the war, but if you are modelling a specific crew, i.e. Wittmann's, this needs to be correct. I suspect that because (a) this Tiger is from 1943, (b) they were a much photographed crew due to their prominence, they would be wearing regulation clothing. There are loads of Wittmann figures available (at least two from Dragon, there is also the sitting figure from an earlier Tiger kit), however most of them seem to be from the Normandy era. In action, Wittmann was renowned for his lack of sartorial elegance, appearing on occasion in scruffy overalls topped with a woollen fleece-like garment; or a nondescript leather jacket, all without insignia.
Regarding insignia, this is probably the most noticeable difference between SS and Heer crews. Heer figures will need the chest eagle and collar death's heads removing and replacing with the sleeve eagle and SS collar runes (right patch) and ranking (left patch).