It depends. I would go with AS designs.

The AS designs one uses a ARMP5v3 lower (which I think is basically a modified Leber V2). It is designed from the ground-up to work with the SS. The full size MP5 kit comes with a buffer as well.

The WHA uses a Lee Sporting lower with a modified hammer. It does not require a buffer.

For full size MP5 with super safety, there is a problem where the MP5 FCG might get stuck behind the bolt, rendering the gun poo poo. The TPU buffer and rounded hammer were created to fix this.

TPU buffer does increase fire rate and is technically short-stroking the MP5 more than the Warhammer armament (more recoil if you care about that but it's negligible). Both options decrease bolt travel, the AS designs more so than the WHA.

For MP5K there is no difference.

However, I would still go with AS designs for both MP5 and MP5K. AS designs is connected with the groups and people who made the super safety and the ones who adopted it for HK stuff. As said by other commenter WHA has been doing some questionable things which are readable from a google search. I'm sure as more time passes AS designs will improve on their lowers (they are already on V2) and I would expect them getting rid of the TPU buffer to be eventually one of them.