I advise my students to try both and allow them to in the pool. Then they decide what they will use for checkouts. When someone says they plan to do both cool (not cold) and warm water with air travel as a means to get there, I advise an aluminum plate with weight pockets on the cam bands. This allows you to add lead to mimic a steel plate if necessary. Shove the pockets up against the plate and you wouldn't know it wasn't steel.
I've sold and set up somewhere near 100 BPW's over the last 10 years. I've made custom hardware for the harness, modified harnesses to work with some unusual body types, and made custom harnesses in various colors.
While I own jackets, back inflates, and BPW's - the BPW is what I use in open water if I'm not diving sidemount. The jackets get used in the pool and for students. The last time I used a jacket in open water was probably 8 or 9 years ago.
TL;DR: BP/W mostly, always with doubles. There's sometimes I like a back-inflate bcd.
I'm with Jim on this. There's no right answer. Our students get a BP/W with a basic harness and steel BP. I dive a TBCS with adjustable shoulder straps more like a BCD because I have mobility issues in one shoulder after having a rotator cuff repaired.
When I was teaching for another shop, I used a cressi back inflate travel BC because it was more like what my students used. I still like that BC, and I'm taking it on a trip next week. In some ways, I still like my travel BC more than I like the TBCS.
If you want one BC to rule them all, it's the BP/W. If you're making a price decision, BP/W is the right choice as it will last you a lifetime, and it will be half the cost and it's modular. If you get a TBCS, you can make it ~4lbs for travel with a soft plate (that's off the top of my head, I haven't weighed it), you can dive doubles with it in either config (soft or hard plate), and you can do the same with rec diving.
Additionally, don't break the bank buying stuff. It's far more important to master yourself (buoyancy, air consumption etc.) as a new diver than it is to have the best equipment. Good gear is nice, but good skills will allow you to compensate for cheap rental stuff. 99.9 percent of being a good diver is skill. Equipment is never a solution to a skill problem.