I personally think it's very different to SSE. I played the SSE a few times and that's it, I didn't play it after that at all for the rest of the time I played Brawl. I just played the other modes. I really think SSE does not have too much replayability (apart from trying to get all those trophies with the trophy stands which I hated so much)
SSE itself was amazing, but even amazing is been there, done that very soon if there's no good reason to replay it over and over.
Smash Tour on the other hand is a much quicker fun casual game, which you can replay over and over. And there is good rewards each time you play it.
As much as my answer to the OP's question will be controversial, I think Smash Tour is a better replacement. Sure we lose the initial few hours we put into doing SEE as there is no SSE replacement in SSB4. But after a doing SSE a few times I had no want to replay it, but I think I'll replay Smash Tour every so often, in between classic mode, vs matches, All Star Mode, etc etc.
Even though I voted for Smash Tour as the better one, this is really like comparing apples to oranges, both are so different and different crowds liked SSE to who will like Smash Tour.