I'm an average (you might say bad honestly) 2h player, and I'm doing ok against most melee, and especially 1h. They can't really enjoy their weapon speed advantage when I keep on moving on the sides and backwards, since with their shields they are a lot slower than me, even though I got only 15 agi.
Interestingly, blocking seems much easier with a 2hander than with my KAS. With the 1h, I often block down instead of on the side, and it doesn't happen with the GGS. Most of my deaths seem to be either due to being overwhelmed, shot or missing an anticav attack.