OP, we have just started to carry a BTK similar to what you linked to. I went through the TCCC/Post-Engagement Strategies course, which covered first aid for downed LEO, and that was what was issued. It came with a SOF-T wide turniquet, quick clot gauze, pressure dressing, and a pair of latex gloves, in a handy package.
As for which turniquet, I carry one CAT and one SOF-T (issued with the kit). I am a fan of the SOF better, for a few reasons:
1) metal winless feels much sturdier than the plastic of the CAT.
2) Buckle > velcro. While both are similarly easy to render buddy aid with, the SOF was much easier to do self aid. With a GSW to the leg, the SOF let's you unbuckle,place around leg, then rebuckle. The CAT involves feeding velcro through a clip,which in the middle of a firefight/bleeding out, it's not something I want to do.
3)It's the one WE carry. Familiarity can be key, so whichever you choose, make it uniform.
The one thing that the class skipped on was the location of the pouch. We are only rewired to carry the TQ, not the whole pouch (some of our cops push back against stuff for stupid reasons). That said, it would be smart to have everyone keep it in the same, or similar, local. Myself and my partner both wear them on the strong side of the bucks of our belts. Considering these kits are for the wearer (I get shot, he's using the stuff off my belt, not his), it's smart to keep everyone in the same place. I'd hate to have to fish around for your TQ if you are bleeding out. BDU pocket? Vest? Patrol bag? Trunk? When seconds count, having that pouch right up front can and will be a lifesaver.
Then, we get into the 1 is none, and "go high or die", but that may be a different conversation.