See in your glxinfo: is direct rendering enabled, and who drives OpenGL? Show the result of
glxinfo | grep 'rendering\|server glx vendor string\|OpenGL version string'
direct rendering: Yes
server glx vendor string: ATI
OpenGL version string: 4.4.13374 Compatibility Profile Context 15.20.1013
This seems ok. One thing I can suggest, look about "Compositing type" (OpenGL, possibly of several versions, XRender), for example see this old Kubuntu discussion (it is not exactly what you need, but it is short and clear for start). I don't use Ubuntu, so I cannot exactly say where to find this in your system...
If this doesn't help, this is really problem of drivers. In principle, a situation when AMD card is weaker than Intel card is possible, but I don't believe in this...