One small addition to Alistair's information: Mississippi Queen is propelled by her sternwheel, but she does have thrusters for movement sideways. MQ's engines were built new for her from plans for a powerful set built in the 1930s for a towboat.
American Queen, on the other hand, can't get out of her own way using her underpowered steam-driven stermwheel; she is dependant on diesel propellers for propulsion assistance as well as thrusters for docking, etc.
I also have to mention the excpetion to Alustair's quite accurate statement about sternwheelers in Europe. There was a modest-sized sternwheeler in Germany years ago; she had quite pretty moulded hull, not at all the flat-bottomed sort of the Mississippi steamboat. She was, I believe on the Elbe; I think I saw her photo on a web site that also included the steamer Hugo Basedow. If I can find the URL I'll post it.
It's worth reminded folks that in the heyday of the Mississippi system, the sternwheeler was the lower class steamer. All the prestigious packets were sidewheelers, i.e. Natchez and Robert E. Lee. Sternwheelers were, I believe, happier in very shallow water, and that's the kind of river one normally would find them on. But sidewheelers were faster. Neither would be a joy to steer as compared to a propeller ship, as there was no propeller wash acting directly on the rudder(s). That's why paddle steamers have such big rudders as compared to propeller steamers.
As it happens, almost all the surviving American paddle steamers are sternwheelers; but the President, still afloat but not in service, was built as one of the last (or the last) bug sidewheel packet.
Bill WOrden