Shogi is probably the closest historical game in terms of complexity to Go. Some of the larger variants might exceed Go's complexity if played with drops, though that's not normally done. And Go played on a 9x9 board (like standard Shogi) has a substantially lower state space complexity (and almost certainly lower by other measures as well.)

But shogi is much more obscure outside of Japan than go or chess, so it gets less interest, especially in the large-board variants.