Why is my compost like wet, black clay?

I have 2 composters. In one of them, the texture of the finished compost comes out kind of like rich loam. In the other, it's like big hunks of black clay sitting in liquid. It seems consistent that it's the different bins, but I wonder if it's actually a mistake I made in one of them. Does anyone know how to prevent this problem and/or what to do now with my wet, clay-like compost lumps?

Sounds like two problems. Definitely too much moisture - needs less water, more air, or drainage or all of the above. Second problem might be too much green nitrogen-rich stuff and not enough brown carb-rich stuff. To break it up, you might try sieving it. Or you could be lazy and put it someplace where it will alternate freezing and thawing all winter, that is how mother nature breaks up lumps. Just don't put it in a spot that will collect liquid and get it soggy again.