IMHO, the Quake derived engines always had superior control and network play. No non-quake derived FPS I play with massive numbers of players feels as "smooth" as the Quake engines. Moreover, I doubt that the Unreal engine has as many licenses as the the various Quake engines. Add up the licenses of Q1/Q2/Q3 vs Unreal/UT, it doesn't compare.
Tim Sweeney is the better artist and toolmaker, putting nice touches on special effects within the engine and the scripting APIs to use them, and lots of content creation tools, but I believe JC is the better scientist/engineer. JC spends way more effort on the research and engineering implementation of better visibility and lighting algorithms, which, aren't as exciting or gimmicky as caustics/procedural textures/etc, but lay the foundation for a much more powerful engine.
While TS is messing around with making models with facial animation, adding flamethrowers, and fog effects, JC is revolutionizing the way FPSes deal with lighting algorithms. (I'm not saying Carmack invented the algorithms he is using) IMHO, Sweeney seems to make better icing to put on the cake, but Carmack bakes a better cake.
I'm frankly not impressed by UT2k3 or Unreal 2. It just looks like the same engine, but with much higher polycounts and special effects. An engine with a unified lighting model, full realtime shadows everywhere, and models created with hi-res normal maps simply looks way better and totally changes the atmosphere of the game. Lighting is the most important thing in 3D graphics, and UT2k3 simply doesn't improve the state of the art. Once you walk around in a game with full shadowing, walking around in Unreal2/UT2k3 will seem a flat experience.
Moreover, JC shows that his prowess doesn't just extend to graphics, but his problem solving skills are good in other areas as well, like network programming, which ID got right very early after JC took over the network code. JC even network gaming issues down to buffering problems in Cisco routers and modems, and his comments/findings were used to modify the routing algorithms used in some routers.
ID doesn't make good games, but when 3rd parties license the D3 engine, like Rogue, etc, the resulting games will probably look incredible. Epic seems to have better artwork out of the gate.
I don't want to lionize JC too much, but I think he is much more of an engineer than TS. TS has talent, but it's a different kind. JC is the kind of guy I imagine to invent something cool, implement it, but hand it over to others to make it pretty. TS on the other hand, I think is better at making lots of little tools and enhancements all over the whole engine.
I guess I would sum it up like this:
JC = Depth in one area (e.g. visibility, lighting)
TS = Breadth in many areas, modeling, animation, special effects, tools, etc