I think Smash 3DS will have a stronger online community. Gaming on the go and portable-wise will inevitably have less lag.
but as for live competition, it will be interesting. I for one have a "gut feeling" that Smash 3DS may indeed be the better competitive game. Regardless of whether it is or not, I think it will be very popular live. I think Smash 3DS will be majorly popular at tournaments, and I don't think lag or connection will be an issue.
However, I think that doesn't mean it will be clear of issues. It will be harder to record (we'll need some 3DS to record stuff for live streams), harder to keep track of (unless every 3DS is on "a big board at a tournament), and it will overall be harder to see everything.
Hopefully, Sakurai and co. give us tools to record all of our matches and share them easily (perhaps even the ability to pause a match and use the touch screen to say replay stuff or edit stuff), and that we as smashers figure out ways to get over this, with things like like cords that show what's happening on TV screens, computers, and live streams so we can share it. If the Smash 3DS scene can prepare for and topple that problem, especially if said equipment for large tournaments comes at a fairly reasonable price, then the game will have limitless competitive potential.
If that happens, Smash 3DS will be a great competitive game that will be easy to share, and easy to enjoy. However, I got a feeling recording all the big matches will become something of a hassle. Perhaps we'll continue to see 3 stock matches to speed up tournaments because of it (like in Brawl) instead of the standard 4 stock matches we have in Melee and Project M (and often Smash 64), which is what I think we'll get in Smash Wii U tournaments.