We are arriving in Vienna from Budapest by train. We are going to be staying in the center of town at the Intercontinental (great price on Priceline) near the Stadtpark. Are we best off going to the Vienna West Banhof or the Vienna Sud Banhof??

Where you arrive in Vienna depends on which station you leave from out of Budapest. Trains arrive at both the East and West stations; there are public transport connections out of both.

You can check schedules yourself here:

http://reiseauskunft.bahn.de/bin/query.exe/en

My apologies: that should be the West and South stations in Vienna.

We are leaving from Budapest-Keleti at 17:50 but the train stops at both stations in Vienna . It's stops at Wien Sudbahnhof at 20:41 and at Wien Westbahnhof 9 minutes later.

The train from Budapest stops only at the Westbahnhof. The 20:41 connection into the Sudbahnhof requires a change of train in Bruck an der Leithe.

It matters very little at which station you arrive. If you want to travel by public transportation, you can take a U-bahn from both stations. If you go by taxi, the Sudbahnhof is somewhat closer.

I would opt for the Westbahnhof, since it doesn't require a change of train.