how old is max?

I would say older.

Max's job as a parking valet means he is college age. True, HoM has Max without a car and dating Roxanne, which contrasts with what happened in AEGM, but one could explain away that it wasn't Max's car that got him to college and he rekindled his relationship with Roxanne after the events of said movie. This does mean Max is probably working in his spare time.
Personally, I would think the best evidence of HoM happening after AEGM is the state of Max's relationship with dear ol' dad. The two are clearly getting along in HoM. Goofy has learned his lesson about meddling in his son's life. In 'Max's Embarrassing Date' it's Goofy who demands the gang give Max privacy in his dinner date with Roxanne. In 'Goofy for a Day', Goofy is adamant about Max doing his waiter job on his own (except when Hades tries to abduct him to the underworld), until Max DEMANDS his dad's help. And Max has definitely mellowed out from his behavior in AEGM. He respects his dad as an authority ('Max's New Car'), realizes his pop can do a better job in certain matters than he could (Being a waiter in 'Goofy for a Day'). Also, he is willing to hang around with his dad, whether its fishing in the snow, joining Donald & nephews in a sled-trip down the hill, or joining in a group-imitation of a seal ('Snow Day'), things AEGM Max would NEVER do.

I'm pretty sure House of Mouse probably takes place somewhere during Max's first year of college or maybe even his last year of high school, you can never really tell sometimes in Disney continuity. Same thing goes for Donald's nephews. I always wondered if they're supposed to be the regular kid versions or the versions from Quack Pack but with the old school 'duck' voices.

"You win some, you lose some. But you live, you live to fight another day."