Nothing at Walt Disney Imagineering ever dies, so some of the concepts used for Western River evolved into a roller coaster ride, which became Big Thunder. But for reasons I'm not familiar with, Disneyland got its version done first. (Maybe TH or another reader can jump in with that.)
The biggest difference in the two rides is that the tracks are mirror images. On Disney World's Thunder, you turn left after the crests; at Disneyland, you sweep to the right. Disneyland's outdoor queue runs under the tracks and through the town. Disney World's indoor queue stand over the tracks, creating space for the steam pools.
Disneyland's mountain is supposed to look more like Bryce Canyon, and Disney World's like Monument Valley, but that's a tough difference for most people to pick out.
Who knows what other factors may have been in play. Perhaps, from a planning and operations perspective, the Mouse may have felt there was a greater need for added capacity on the east side of the park (sure would seem that way). Maybe someone was also trying to appease Marc Davis, whose Thunder Mesa was surely going to be the big loser if Big Thunder was built. Sounds funny given how giant and results-driven the Disney Company has become, but back in the 1970's guys like Marc Davis and Card Walker and Marty Sklar had all known each other for a long time.
Or maybe Disney was hedging its bet. Roller coasters were pretty unfamiliar territory for Mickey. Though it was evident that coasters were a big, big draw for park audiences and Disneyland had run the Matterhorn successfully for more than a decade, you have to imagine there was some trepidation in the Mouse House about going with a full-on (albeit a tame) coaster ride instead of a lavishly themed dark ride on that plot of Frontierland. Space Mountain was still themey, and it was positioned as a Walt concept. So maybe it felt safer?
Either way, I think after Space Mountain opened to huge success at WDW and Disneyland's BTMRR was received well, the writing was on the wall.