H.M. Screw Steamer Niger Towing the Paddle Steamer Basilisk, 1849
As much as I like a sternwheel, I'm certainly under no illusion that it in any way is superior to a propellor as a means of converting BTUs of thermal energy into usable thrust.
Any advantage they might have over a prop, (besides a fun/nostalgic/romantic experience,) is the ability to operate in stretches of shallow water that in the old days was usually filled with snags, and the ability to nose right into the banks to load/unload people and cargo.
They were also more maneuverable in tight channels than the early single-screw prop boats.
Here in the NW, small paddle steamers would work their way up small tributaries in reverse where there wasn't enough width to turn the boat around.
A pic in a book I've got shows a small steamer with a horse drawn wagon next to the boat.
Without any roads, (that didn't turn into mud pits at the first rain,) this method of getting product to market was common.
We think of those big Mississippi river boats, but there were hundreds of little 40>60' steamboats carrying goods/people all up-and-down the small rivers.
On the Columbia River the steamboats "last fling", so to speak, was hauling the materials up-stream to build the railroads on each side of the river that would put the boats out of business.
With dredging, sea walls, no snags, and developed facilities, the propellor boats could take over for barge traffic.