Given the astonishing constraints of time and budget that a little vignette like this must face, I have to give Steven Moffat kudos for pulling off as much characterisation and even perfunctory plot as he did.
I’d have rated this as a bit too flippant and self-referential, except that the final conversation in which Tennant paid tribute to Davison adds a dollop of weight to something that is, by design, complete fluff. Also, self-referential is really the point when you have two Doctors from 20 years apart meeting. This is basically a non-stop series of fannish references and gags. Doctor Who: The Vaudeville Routine, perhaps.
Peter Davison doesn’t entirely seem to remember how he used to play the part, but there’s enough of the old spark there to make things worthwhile, and it’s not entirely stretching the point to argue that the two incarnations have a certain affinity. Janet’s very partial to the “When I was young I was old and crotchety, then I got older” bit too. (She’s suggesting now it could be a Merlin reference. Hmmm. Possibly.)
EDIT: Also I wonder if the “You were my Doctor” is Tennant or Moffat speaking through the character? In many ways Davison was as much ‘my’ Doctor as Tom Baker, and I have very fond memories of his era, probably the last in which I truly enjoyed the old series.
EDIT 2: From the Doctor Who Confidential online it seems clear that RTD and Phil Collinson, and even David Tennant, are all huge Peter Davison fans. The sight of them all geeking out behind the scenes probably made me feel fuzzier than the actual mini-episode.