I was out there a couple of years ago and did the canal/river trip you are proposing. I think that there is only one operator running the boats.
The trip follows a circular route with pick ups/stops on the canal (about a mile from Vienna city centre) and again on the main part of the river. From memory, the complete circuit takes around 3 hours. The boats provide a bar and restaurant service – but I can’t say that the scenery is that inspiring. However the hydro-electric barrier across the Danube impressed me – as we passed through the lock, we were joined by one of the enormous commercial barges that ply the river. There is a further smaller lock bringing you back on the canal.
I don’t know of any web sites to the operator. I can’t remember the price of a ticket, but recall it being recommended to me as a bargain price (for the trip).
My advice would be to check out the likes of Trip Advisor for more information.