I think, from the viewpoint of a mathematician, there has been more progress in solving Go than in solving chess. http://math.berkeley.edu/~berlek/cgt/go.html shows some progress on generic Go endgames; I've never seen something similar for chess. It all is either a smart exhaustive search, or the use of heuristics that humans think can be used to value positions. I am not aware of any research on the validity of such heuristics.
Because of that, I think chances are we will solve Go before we solve chess in the mathematical sense (at the same time, I think chances are effectively zero that I'll live to see either happen). Yes, chess has a much smaller search tree, but it is inconceivably large to start with, and its rules are ugly. That means that any mathematical breakthrough will likely have lots of ugly special cases (even ignoring rochade and en passant). Go, in contrast, has a much simpler structure.
Because of that, I think chances are we will solve Go before we solve chess in the mathematical sense (at the same time, I think chances are effectively zero that I'll live to see either happen). Yes, chess has a much smaller search tree, but it is inconceivably large to start with, and its rules are ugly. That means that any mathematical breakthrough will likely have lots of ugly special cases (even ignoring rochade and en passant). Go, in contrast, has a much simpler structure.