They do have the exact same bike rental system as Mexico City. But I did not feel like taking my passport down to one of two offices and getting the card. Vienna is a very big city, my interests were spread all over the place, I did not set up time for a bike rental adventure. So I went for the public transportation, very very easy.
I have to say though I was sad that I didn't get to utilize the lanes for bikes only, created inbetween the sidewalk and streets. I also trekked out to the Museum Gugging, the bike path was almost entirely along the Danube river, but so was the metro/bus so next time I'll get the bike.
We got these bike lanes too. I was very impressed.