The only character I'd be interested in seeing crossover to TO is Elena, maybe Katherine (though preferably for awkward team ups with Klaus or Rebekah than anything with Elijah) and extra maybe Stefan since I do like him being flummoxed by the Originals. Tyler would have been really near the bottom of my wish list for crossovers. Among the easiest to justify, but...it's Tyler and I really don't care.

And going the other direction I think Elijah guesting on TVD is easily the least possible option for a while even though obviously he'd be my top pick (kind of, in some ways better to keep him away and imagine ways he could return than actually see it where it would probably mess things up form wishes).