I imagine that a fretted A on the E string is better than an open A on the er, A string. It is definitely tonally different. But if needs must I'll play open strings, no problem. Sometimes it's just a lot more difficult to play certain lines without playing open strings. And as for muting, if like me you're mainly a pick player and use palm muting, then muting isn't an issue. I would say though, that during my brief dalliance with five strings it was clearly a lot easier to avoid playing open strings, if you really wanted to avoid doing so.
One thing I liked about five-string basses was the ability to play lines without moving around the board as much as you sometimes have to with a four-string. And it's easier to transpose keys. What I didn't like about five-string basses was the extra weight, faff and expense just for a few extra notes. So I went back to four strings and am perfectly happy. Well, happy with four-string basses, that is - I'm a miserable, grumpy git otherwise, obviously.
Edit: Just thinking about five-string basses has ignited 5-string bass GAS. D'oh!