Are you dead set on those two choices? Neither are especially good, grippy cars out of the box as they are GT cars at their core. Of course anything can be made into a grip car but you'll be spending a few grand on top of your £6k.
The alternative option is that £6k will get you a nice 350Z, which is designed to be more of a sportscar out of the box.
Much more modern car & chassis than both the R33 or the S14, nicer interior, arguably better looking, and V6 noises beat RB noises any day of the week in my opinion
If you can get over the non-turbo stigma and the BHP willy-waving, and you don't need rear seats then it's a seriously good car to consider. A few people on here have moved on to them from S-bodies over the years and speak very highly of them indeed (Docwra, Fake Ben Taylor, and Fridx for starters).
I've been passenger in a couple of the above ones at SXOC track days too and they are a lot better than I ever would have expected, so if it's a grip setup you're interested in then I would give it some serious thought.