I would count myself amongst the crowd who thinks Hamlet is older. I base my belief on the following conversation that takes place between Hamlet and the 1st Clown, who is the church sexton, a grave-digger, the church cleaner and bell-ringer.
Ham. How long hast thou been
1 Clown. Of all the days i' the year, I came to't that day that our last King Hamlet overcame Fortinbras.
Ham. How long is that since?
1 Clown. Cannot you tell that? every fool can tell that: it was the very day that young Hamlet was born,--he that is mad, and sent into England.
Ham. Ay, marry, why was be sent into England?
1 Clown. Why, because he was mad: he shall recover his wits there; or, if he do not, it's no great matter there.
1 Clown. 'Twill not he seen in him there; there the men are as mad as he.
Ham. How came he mad?
1 Clown. Very strangely, they say.
Ham. How strangely?
1 Clown. Faith, e'en with losing his wits.
Ham. Upon what ground?
1 Clown. Why, here in Denmark: I have been sexton here, man and boy, thirty years.
According to the preceding Act V.i conversation, the grave-digger has been in his occupation since the day Hamlet was born, which he eventually gets around to saying has been thirty years.
Some may argue that Hamlet must be younger since he is in college and he behaves so immaturely, but Gertude and Claudius don't behave much more maturly. Moreover, many people are still pursuing university degrees well into their thirties.