QT has a really bad X11 backend, that could be a problem. I doubt Eagle is using OpenGL, i guess its simply causing software fallbacks by using too advanced QT drawing routines.
However thats all speculation. Best would be to install debugging-symbols for your whole OSS stack, and use a system-wide profiler like sysprof to see whats really going on behind the scenes.
Everything else is pure speculation and a waste of time.