I've got a Superlight R (just being converted to 1.9 Scholar block and 240+ bhp...), sold my LHD 964 RS last month (owned for a year and a half) and bought a LHD 993 RS Clubsport a few months back. I've driven a 996 GT3 on track too. So, I'm your man!
The Caterham will almost always be the quicker car; the twistier the circuit the faster. The Caterham also has the more benign handling. I found my 964RS a much more challenging car to learn to drive and I only scratched the surface. That makes it a challenge to be enjoyed by the car fiend and I imagine that is the idea/appeal.
The 964RS has beautiful steering. Best in LHD with no power assistance (RHD does have power). It is a lovely thing through which to commuciate with the road. It is very close to a Caterham in concept; it's light, responsive, dives for corners, very much the race car for the road. A RHD car is possibly £50k though, a supply and demand thing. LHD is more like £35k and some would say the true RS!
That being said, I chopped the 964 in for a 993. I borrowed a 993RS for several months and loved the slightly more user friendly handling. It is easier to feel a better driver, with less chance of meeting Armco, in a 993; it's a technology thing with the rear suspension set-up in particular. I got the Clubsport as it's the last of the aircooled road racers.
Onto the GT3... Now, without upsetting a lot of people, it's just not as raw as a 993/964 RS. That makes it further divorced from your Caterham. It's a lovely car, but I see it as an everyday car, something you cruise motorways in on your way to a track day. Some think that mad, but going from a screenless Caterham, screaming to 8000 revs, to a 964RS seemed like the ultimate in comfort. Try for yourself, but I think you might find a GT3 a little too inert/detached. That's what I felt. Clearly it's not like a Mondeo and is a splendid car (and v good value now), but it's no tactile RS.
James