In terms of mathematical complexity, of course go has more positions, more complexity. But as limited as humans are we'll never master either in terms of perfect play, so in practical terms both are "infinitely" complex.
In terms of ratings some try to show that Go ranking (say 10kyu through 9-10 dan) number about 20 while chess classes (200 point jumps) go only from 1000-2800 which give only 10 levels. Therefore go is twice as complex in practical terms... but this is a pretty flawed comparison. For one thing in go there are no draws, I believe white starts with 8.5 moku (correct me if I'm wrong) for being second. Because the half a moku there are no ties.
Chess has no such corresponding feature. In fact it's draw margin is quite notable. This means to go up a class in chess (win 75% of games vs 1 class lower) represents a large increase in skill, whereas in go a rise from 6 kyu to 5 kyu does not represent such a large leap.
I find go fascinating, but had to make a choice between the two. I chose chess because of where I live I'm able to easily go to chess clubs and tournaments whereas with go I would be learning largely on my own with little guidance and little OTB competition. I've played maybe 50 games (7-8 years ago) and know only the rules and very most basic ideas.
My brother tried getting a bit better at it, but only kept it up for about 6 months. He was able to find some great games of go played in the past by the equivalent of a super GM (9- dans) and even the basic explanations (of course that's all I could understand anyway) made it obvious the strategy goes very very deep. A great game for sure.
I love the stategy involved in playing chess and the analogous similarities of chess to real life. However, for several years, I've been wondering if the game of Go was actually superior in these two and other areas. Knowledgeable input requested.