Total game states is one measure. What does it take to solve the game?

You can also look at the branching factor, how many moves are there to make on average. For chess, it's 20. For go, it's something like 300.

You can also look at how long it takes from a move to seeing its negative consequences. A bad move in chess is frequently visible in very few moves. You lose a piece. You lose an exchange. Often these sequences are virtually forced. By contrast, the consequences of a bad move in Go are usually not visible for 50 moves or more. And there is nothing forced about the sequence that gets there.

You can also look at how likely good players are to play similar games. Many chess games have been played over and over again. People sometimes play half the game out of a memorized opening sequence. By contrast, it is plausible that no Go game has ever been played twice on a 9x9 board. It is very unlikely that any Go gamme has been played twice on a 13x13 or 21x21 board.

You can also look at how big the skill gaps between humans get. In my experience, a 1 stone difference in Go is roughly a similar skill gap to 200 points of Elo in chess. A rank beginner who barely moves the pieces may have a 400 rating. No human has ever reached a 2900 rating. That's 12.5 levels. By contrast Go has 30 levels of amateur (kyo), another 9 for serious players (dan), and then the skill range among professionals is about another 3. That's 42 levels of fairly recognizable skill differences between humans. Which speaks to how much more there is to learn about Go than chess. (Even more so when you realize how much of advancing in chess is a matter of making fewer mistakes. By contrast advancing in Go is much more about integrating better principles.)

No matter how you look at it, Go is much more complex than chess.