Emscripten can now work with Clang. It turns out that the llvm bitcode that Clang generates is slightly different from that of llvm-gcc, which uncovered various minor bugs and missing elements in Emscripten (for example, the 'phi' command).
All the tests now pass both llvm-gcc and Clang, and with both optimization and relooping on (however, relooping has been weakened, due to some bugs that were discovered).
The benefits of allowing Clang to be used is that having two sources of LLVM bitcode is better than one - more chances to catch bugs (but even more important would be to add non-C/C++ sources of LLVM bitcode as well!). Another benefit is that Clang is simpler to build so it will allow more people to play with Emscripten.
The wiki has been updated with full instructions, so you can get Clang and try it out with Emscripten right now.