Can White get a theoretical advantage against the Sveshnikov Sicilian in today's theory? I'm looking for an opening expert or an experienced Sveshnikov player that knows the answer to this.

The Sveshnikov has been increasingly popular and it has also proven to be very good for draws. However, is there a line that like grants an unclear line that will give White a chance to fight for an advantage?

Also which line is considered better for avoiding a draw, the Bxf6 first line or the Nd5 line?
Let me answer your second question first: According to chesstempo db there are 6% less draws after 9.Bxf6 than after 9.Nd5, with White and Black each getting 3% more wins!
As far as a theoretical advantage: hoacin's comment is accurate.  Of course like all openings it is more about heading to the positions you like or are more comfortable with; thus many GMs would say that 3.Bb5 is the best move against the Sveshnikov.