Worth knowing, is that beavers, when crowded, will travel vast distances over land, to find a 'better place'. Have pictures of ones that ran into miles of chainlink, and were trudging back to source...
Have dealt with both Beavers and Muskrats, and can say that I'd rather have beavers. The Muskrats tunnel under the shores, and the tunnels then collapse, making a right mess. They tunnel into dikes as well, and make a right mess. But, muskrats don't cut down trees.
But, neither are all that hard to get rid of, if you are willing. I shot Muskrats with anything from a .22, to a .308, as well as a LOT with a shotgun (use goose loads). As destructive pests go, I'll nominate the rats as worth more effort. Beavers are pretty predictable, and easy enough to deal with, with a .22. Get their attention by opening a waterway, or simply pattern then and learn their habits and get them from shore when they swim by.