I infrequently hunt deer or target them specifically as they are mostly incidentally taken while hunting elk but I've used a 308win a good deal for both with good results. At current I'd classify your 350rem and the 358win as cartridges for folk who load their own and the 308win is more of an factory turnkey option. That's really what it comes down to.
Currently the BLR in 358win is an discontinued item. If you want one you best aquire it as they'll get less available in time whereas anything in 308win is always available.
