For me, it's probably the lack of an SSE-esque mode, especially since so many recent Nintendo games have made strides in the co-op platformer/action game genre, and Smash Bros easily could have.
On 3DS, Smash Run is a pretty good substitute, though it's kinda marred by the fact that I cannot play online, and there is only one map (though it does change randomly each time, which I like). Also the fact I cannot make the timer longer, the final battles longer, or even choose the events. And the fact that due to there being no direct player interaction on the map, and having two Final Battle events that also don't have player interaction, you can potentially play this with your friends and never actually interact with them. I still quite like Smash Run, but these things hold it back from being the huge selling point it could have been.
However, the Wii U version has nothing to satisfy my Smash-adventuring needs. It has Master Fortress, which shows they THOUGHT of this kind of mode, but Master Fortress is a linear level that I need only play once, plus I have to fight the CPU and some bosses for a while to get to play it at all (meaning players who are not good at Smash but like things like SSE will never get to experience Master Fortress anyway - and it doesn't show up in co-op).
This may seem unimportant to some, but I think a mode like SSE (even if it didn't have a story and was just going through various themed levels from Nintendo games in a big adventure) would have been really good for the Wii U version. It would be a great way to show off the some great visuals on a larger scale (the Smash Run map looks great on 3DS, even), great for co-op, and would probably be less tedious of a single player experience than going through Classic, All-Star, and Special Orders with every single character. It would also be great for breaking up the time spent in these modes when trying to unlock stuff.
I want to 100% Smash Wii U like I almost did Brawl and like I have done on 3DS, but going through Classic and All-Star with every character after only doing so within the last month on 3DS, seems like it's a bit too tedious. The Wii U version should have really had some kind of Adventure Mode to help the single-player experience feel as fresh and new as everything else in the game. Yeah, Events are cool and all, but you can complete them all in an hour or so provided you never fail, and once you finish them all on hard mode, you never have any reason to come back to them.
It's really ironic that the thing I am most looking forward to when playing the new Project M, is going through Subspace Emissary with the Project M mechanics.