I think this topic confuses two things.
People who think that “Go is far more complex” has the meaning that “Go is a lot harder / more interesting / profound than chess” are misunderstanding what is really meant when it is stated that Go is more complex. Complexity in terms of game trees has not really much to do with how difficult the game is for humans, but instead just is the measure of how many possible games there are. In this sense, Go is indeed vastly more complex than chess, since there’s vastly more possible games. This doesn’t imply that it’s either more difficult for humans to learn, harder to solve (by finding a perfect strategy), or harder to write a strong algorithm for (like AlphaGo).
See “complexity” simply as a measure of how much resources is needed for something.
- Complex things for humans (like Go, chess, playing the piano, learning a foreign language) need a lot of resources for humans to get good at.
- Game complexity measures how many possible games there are under the game rules, or how many board positions, etc., and is useful to determine upper bounds to how hard a game is to solve: if we want to find out which player wins the game under perfect play, we could consider all possible games and just compare all results.
- Strategic complexity measures how difficult it is to formulate a perfect strategy to win a game. If we have access to the whole game tree, we have access to a strategy, but it is not always necessary to compare the whole game tree. For example, the game Hex can be played on a board that is far larger than a go board, and thus for such boards has a far larger game complexity. But, by a strategy-stealing argument, it can be seen that the first player will win the game under perfect play, thus regardless of game complexity we know who wins.
- Computational complexity measures how resources increase as the problem gets larger. For example, in Go it would measure what the ratio is between the amount of time (or space) needed to solve an NxN board and to solve an (N+1)x(N+1) board. For example, the resources needed to let a computer solve a game of Go grows exponentially in time and space (and because the game is EXPSPACE-complete, it is quite likely that this is the best we can do, but this problem is very hard to solve and related to one of the largest open questions in mathematics / computing science). Similarly, solving a game of chess grows exponentially with board size, but Hex, for example, does only grow polynomially.
So to summarise, stating that Go is more complex than chess because the game tree is larger is just a fact: Go has a larger game complexity. Stating that Go is more difficult to solve strategically than chess is unknown, since neither chess nor Go have been solved strategically yet. Stating that Go is computationally more complex than chess is incorrect, since both are equally complex to generalise to larger board sizes.
Finally, saying that Go is more complex for humans to learn, is just an opinion. Considering that there is no definite point reached by any human for “having completed learning Go”, I think it’s a bit nonsense to think about how hard it is to learn Go. It’s as hard as you want it to be: in practice there’s always a stronger opponent waiting for you.