The guy stated he's not expecting it to have Cancun nightlife so I'll try to reply something helpful rather than just saying Cancun when he's stated his interest in Playa Del Carmen.
I'm 21 and have been on nights out in Playa Del Carmen and Cancun. As you've said you realise they are not the same but this doesn't mean they're not as enjoyable I'm sure you'd have a great time in PDC. We loved the Blue Parrot as much as we loved Coco Bongos even though they couldn't be more different! There's drinks a plenty an indoor dancefloor made of sand and an outdoor dancefloor on the beach, the music is high and the atmosphere is great - I'm sure you'll all love it!
There's loadsa little places around PDC but Blue Parrot we thought was best although we didn't try the Clubs last year - we intend to next year though.
Also you can get to Cancun easily enough for nights out. This is what we are doing - having the benefit of the nicer hotels/resorts in Playacar and planning on splitting our nights out between Cancun and PDC.
As for which hotel is best for you I really can't help you on that....We stayed at the Allegro last year...it had some young elements - ie. Tequila Darts, Beer drinking competitions etc but it wasn't like that all the time and was nothing to crazy - it was a fun place though. However now I think the beach is gone and possibly it is closing down.
We're staying at the Tucan this year but I'm not aware that it is particularly 'young'.....
My advice would be pick your hotel based on the grounds/resteraunts/location/beach etc rather than whether it draws a young crowd cos I'm not sure if there is such a hotel in PDC but I could be wrong!
Hope this has helped! x