Mosses are not really fast growers when compared to other plants. That said, the growth tends to go unnoticed until one day you realize that you need to remove a few pounds of it.
Java moss is good for attaching to rocks and wood. In fact, it will pretty much attach to anything given enough time. For this reason it can get annoying because strands tend to get loose and start growing wherever they land. I limit it in my main tank to one small area of driftwood only because my cherry shrimp are attracted to it.
Christmas moss does not attach to things in the same way. I usually place it where I can lightly wedge it between something to stop it getting knocked out of place. In my tank it tends to grow vertical and gives quite a good effect.
Both of these mosses are green. Java moss is darker. That's the only two mosses I've had experience with. They are very easy to keep.
If you look at my main tank in my profile page you can see the christmass moss at the bottom right of my tank. The java moss is on the arm of driftwood left of center.
HTH