Ever seen a karate instructor working with a white belt that was the same age as them or even older? The student is still considered a "pupil." And even if you wanted to say that the title pupil should only be reserved for younger students in this sense, it could be Obi-Wan's way of subtly demeaning his treachorous apprentice in his own mind.

But since the whole thing is revealed to be a lie by the end of ESB, Obi-Wan's revelations to Luke in ANH about Vader aren't holy scripture. What we see in the original ghost scene of ROTJ does seem to indicate they were roughly the same age.

So no matter how you want to approach the OOT when ignoring the PT, there's only evidence for Vader being old.

And if you want to go by just the original Star Wars (1977), without the retcons of the following films, we don't know enough to conclude either way.