It's a shame that Photoshop from over 10 years ago still wipes the floor of the Gimp today. Sadly, that is why free software will never ever compete with commercial software of any caliber what-so-ever...
Generally, though not always. If there's any one high end open source application that can stand toe to toe with them, it'd be Blender. Over the last 4 years, it's gone from a terrible thing only FOSS zealots and the desperately poor would use to absolutely fantastic. It's so good in fact, if the Blender Foundation spent a couple of release cycles smoothing off some of its rough edges rather than constantly adding new features, I'd consider it a better choice than Max and Maya.
I guess it all depends on who you've got working on your project. Blender seems to have dozens of the best and brightest working on it night and day, whereas GIMP is a couple of talented guys who only get to work on it in their spare time. Hence why the former seems to improve by leaps and bounds every three months, whereas the latter moves at a snails pace, seeing big releases every two years or so.