No, LLVM/clang is all about having a superior architecture to GCC, so that a lot of new applications become possible. One of the key ideas is that the optimizer and code generator are libraries with a C++ API. One cool application of this is that you can use the LLVM library to implement a JIT compiler for your interpreted language: you generate the machine code directly into memory (instead of to a file), then execute it.
LLVM has many more developers than GCC, and is evolving and improving more quickly than GCC can. This is because of the licence: it turns out that corporations like Apple are more willing to provide developer resources for this open source project if the licence isn't copyleft. For this particular project, this means that the BSD license is more successful than the GPL. Of course, there are other projects for which the GPL produces better results in the real world.
If you want to make a GPL fork of LLVM just for the pure pleasure of fucking over the original project due their heresy in choosing a license you don't approve of, well, good luck with that.