I use both of them all the time - but they're different and sound different.
Just playing an open B string gives you A E A B E, the mu major gives you A E B C# E - it contains the 3rd that the other version doesn't. They're both simple as to play if you have the correct sized first joint on your first finger, which I do.
That's probably another interesting question for people - if you're playing an A chord in root position - full chord, all 5 notes A E A C# E, how do you do it? One finger or three?
I always play one finger, and to play the mu major I just slip the 4th finger into place in the position, 4th fret, G string - and that was my original point - I almost do it automatically, when playing a standard A probably would often sound better. And I'm referring to creating my own tunes here, I'm not substituting it in for a normal A in other peep's tunes. Just something I do too often.