The rockwork and overall environment detail is more elaborate at WDW. It's difficult to explain without just comparing side by side yourself.
The interior scenes are very different environments. DL's ride takes place in a darker swamp-like environment. The ceiling is covered with what appears to be hanging weeping willow foliage. The walls are largely not visible, blacked out and obscured. The ride itself is smaller and more narrow, affecting the general size of the scenes. The interior scenes following the first drop are more grouped together into a single room.
WDW's interior scenes take place on a river traveling along what appears to be the edge of a forest. No longer a swamp, but a bright countryside with farmland, rolling hills and blue skies in the background. A bit more like the animated scenes from the movie. The foliage above is no longer willows, but maple leaves (this difference even applies to the Riverboat finale). The scenes have more depth and detail, particularly in the background. A handful of these scenes use some really beautifully designed physical forced perspective scenery. Layered rolling hills and farmland with scattered trees. The walls are now used as a backdrop for brightly lit murals of blue skies and clouds. These first handful of scenes are more spread out and separated from one another.
Disneyland has a few more animatronics than WDW, though WDW has a handful of different figures of its own, some with more advanced motion (such as the hopping rabbit). There's more of an emphasis on Brer Rabbit, Fox and Bear and their plot progression. The trio also have vastly better designs, looking more like their animated counterparts from the film.
The music is also a bit different. Mostly the same songs, but played as different genres. DL is more jazzy, whereas WDW's sounds more like country/bluegrass. Disneyland also has an exclusive vocal version of the Burrow's Lament song in the Laughing Place that doesn't exist at WDW (still played instrumentally but not sung).