Interpretation Or Authenticity? What do you look for?

I was comparing Gustav Leonhardt playing The Well-Tempered Clavier to a version by Helmut Walcha. Leonhardt really cracks through it compared with Walcha. I also noticed Casals playing Suite No. 1 in G major for cello and he emphasises a completely different rhythm to a version by Pierre Fournier I have heard. As a fairly late comer to classical music and certainly no expert I was interested to know if you look for interpretation or authenticity in an interpretation? I presume it depends on t [...]