David Tennant’s Doctor would not face the Weeping Angels the same way Matt Smith’s Doctor would, at least mentally.
The same goes for Eccleston’s Doctor as well as Capaldi’s, and while at their core they’re all still a brilliant time traveler, each one had a different method of facing a familiar problem.
An even greater shame is that we haven’t seen Jodie Whittaker’s Doctor face the same villains, as that’s where the true personality differences between Doctors can be seen.