If you take a look at the timelords of the 60s to the 80s, all of them had a varying degree of being an old codger. The doctor, regardless of the actor's age, would always have an aspect of the 'grandfather' about him.

if you look at the NEW doctors, Eccleston and Tennant, they've all been young, dynamic, and ever so slightly manic.

It only makes sense that they'd take the master the same direction.