Yeah, the '50s reissues and the '50s Classic Player have a "harder" (less rounded, more pointed) V shape than the Baja Tele. I had a Jimmie Vaughan Signature which was also quite a hard V. I've never tried a Clapton Strat but I believe it's a slightly softer, less bulky V and a bit shallower at the nut (a lot of V necks are pretty much the same depth for the whole length of the neck).
It's not so much the V shape of the back that bothers me, it's the shape of the "shoulder" where the neck meets the fingerboard. I prefer a more rounded shape like a Gibson '59. The Fender C is a bit too slim, but still OK for me.