Depends a bit on what you mean by debug, but either way the emulator would be the way to go unless there's a clear indication that there's something ARM-specific going on.
For LuaJIT, cf.
https://www.freelists.org/post/luaji...filer-released
For regular gdb stuff I like the Nemiver frontend, but anything goes. :P See
https://github.com/koreader/koreader...with-gdbserver for doing it on-device.
I've done my profiling on crengine with cachegrind + KCachegrind for visualization. That resulted in some pretty significant performance gains (mostly thanks to @poire-z
).