While we're at this, am I the only one who sees him as Xavi's heir in central midfield? Somehow it makes more sense to me that Iniesta will just back up a bit and take over Xavi's role, rather than Busquets playing more up front, or Cesc backing up. Iniesta is already the one taking over Xavi's duties in the Spain NT, I don't see why he couldn't be our main CM when Xavi starts declining.
He's not the midfield conductor like Xavi is in terms of distributing. He's more into roaming and drawing defenders to find players in positions to start an attack.
While I do see him dropping deeper, he's just too different from Xavi for him to really take his role, and that's not where his strengths lie. Take into account that not every player will be replaced with an exact version of them and our midfield will not always have the same system as the Xaviniesta type thing we have going now.
Thiago is in the mold of Xavi by kick starting the tiki taka metronome and spreading the play to the wingers/fullbacks, starting passing movements, and overall bossing the midfield. He's more attack minded though I'd say. We might even one day see Samper as the deep lying distributor/playmaker and Thiago as the roaming Iniesta-type player, or Rafinha being an advanced playmaker and Thiago being the distributor. We can't be sure yet.