Even though there is probably a lot more afoot than this one reason, game Director Masahiro Sakurai states that since each version of the game features different stages, cross-platform play "wouldn't work," but there will be some interaction by way of transferring customized characters. They won't be costumes, Sakurai said, because he doesn't want to "take away from what makes each character unique" -- which presumably leaves a possibility for ability re-skins or different character colors.
The lack of cross-platform play isn't a deal-breaker by any means, but I enjoyed the feature on the Vita and PS3 with PlayStation All-Stars, as it allowed me to play the game with friends who only bought the game on one platform.
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destructoid's previous coverage: Super Smash Bros.