Personally, I would rather have an Alpkäse than Sbrinz. They are really about the same thing, but Berner Alpkäse is a bit more easy to eat.
Also technically, you cannot make Sbrinz. That is a protected name, and you have to be on one of 50 some farms in Central Switzerland to legally make Sbrinz.
And historically speaking, Sbrinz as it comes from Italy originally referred to Berner Alpkäse, which was for centuries traded over the Alps to Italy. Then the Central Swiss got in on the game later, and just adopted the name for themselves.
There is really very little difference between Berner Alpkäse and Sbrinz. The latter is cooked a little higher and so is drier and harder. There is no real advantage to this though, because the former can be aged up to 10 years (after which time it is too hard to eat).