I think you quoted one such bit once in your journal - something to the effect that Seven (not knowing he's going to luck out in the regeneration lottery via Paul McGann) wishes he'd look handsome once, and then remembers Three as dashing. :)

Ah, yes, one of my favourite bits from The Algebra of Ice. The same conversation where we also find out that Seven has no idea where his accent came from. (Although now that Big Finish has released several audios reuniting the Sixth Doctor and Jamie, maybe he picked up the Scottishness from there.)

Anyway, it mainly seems to be consecutive incarnations of the Doctor that don't get along, which makes sense if you think about what tends to happen to his personality when he regenerates.