GPU and CPU rendering result in different lighting in Cycles.

Literally the same scene. What could be causing this?

a type of HDRI file that is not recognized in CUDA??

What version of blender? This was an issue in earlier 2.79 builds but has been fixed in more recent builds.

All input images should be decoded to generic memory buffer before uploading to GPU so if a file is incopatible it will not work with CPU either.