Steven Moffat says Matt Smith and David Tennant got along famously during the filming for the 50th anniversary:
“They got on like a couple of old women. They just say in the corner and gossiped the entire time. By the end of it, Matt told me that he’d worked out this plan that they’d both continue in Doctor Who: do five individual episodes each and three together – would that be ok?
“It was a nice plan. I think if I’d said yes they’d have gone for it.”
“David and Matt, I think… were both quite apprehensive of the other. David’s continued to watch Doctor Who like the sad old fan he is and so as far as he’s concerned Matt’s the Doctor. And of course for Matt, you don’t believe yourself you’re the Doctor, you just think David’s the Doctor.
“So they were both slightly nervous and slightly apprehensive.”