Yeah, Fallout had to forgo the 80s Cold War aesthetic. The 80s and the Cold War were over, so it wasn't contemporary, but it also wasn't retro-chic either (and still isn't). The 50s Cold War, however, was recognizable as a retro aesthetic, so Fallout went for that.
But even that was a bit tacked on... Fallout still had the "Skum Pitt" and the "Skulz" and other leather/spiked punks with high-tops and shoulder pads, and 80s references in names like "Gizmo" and "Decker," which makes me even question anyone who is claiming that the aesthetic and thematics elements were all that different.
The Rangers were replaced with Vault Dwellers. That's about it for any core differences.
Otherwise, the story, setting, quests, game mechanics, and tone of the game were extremely similar to Wasteland, with most of the core elements of the game directly in parallel to those in Wasteland. If you don't agree, you seriously need to do a quick play-through of each again. It seems willfully stubborn not to acknowledge that Fargo remade Wasteland as Fallout. Same basic game, but in a very worthy rebirth and reworking. The two games progress along the same routes, using two variations of the same general conflicts, characters and locations throughout. Every step of the way in Fallout, you can say, "oh yeah, this is just like the _______ from Wasteland."
Even if you don't agree that Fallout was a remake, I still find it ridiculous to suggest that they are so different from one another that there could possibly be Wasteland 2 that bears no resemblence to any Fallout. A game called Wasteland that bears no resemblence to Fallout would be a far cry from Wasteland. It would have to be Angry Birds using Army Rangers instead of birds. That's about the only possible game I can imagine that has anything in common with Wasteland but nothing in common with Fallout.