I like your comment Mike I had not thought about western philosophy. I see you mention beauty in Go, being a very basic player I find that difficult, although I know much about beauty in chess especially in composed problems.
It is struggle that often creates beauty. Nature in its struggle for survival presents us with endless beauty.
I play both games, Chess at 1750 ELO and Go at 2 kyu. I also enjoy writing programs to play games (Connect 4, Othello, Checkers, Chess). So I felt in a good position to comment.

Chess is a great game. It suits our western philosophy where anything can be treated as a battle. Go on the other hand is more like world politics where it's perfectly acceptable to loose a local battle as long as you gain compensation that can be used elsewhere on the board. I actually think Go is a more beautiful game to look at but then a little understanding helps.
The advantage of chess in the West is that it's easy to find a decent oponent while finding any oponent in Go can be difficult. Obviously that reverses in the East. It's also quite an old game (1500yrs) that has stood the test of time. There are a few disadvantages to Chess - I personally don't like seeing draws (I think the number of drawn games practically killed of checkers) and it gives me an uneasy feeling knowing that computers play our "intellectual" game better than us.
The advantages of Go include a handicap system that allows me to have an equal game against players of widely different skills. Draws are very uncommon. It's also an ancient game most likely created around 4000 yrs ago. I can also easily beat any computer program even though a huge amount of work has gone into the programming the game. The big disadvantage is that just too few people play it over here.
Even taking More's law into account I don't feel either game is solveable and just creating a world champion program doesn't mean you've solved the game. So which game do I play when I go to the pub?
I prefer playing backgammon, preferably for money - go figure!