Not really always. Bards and black mages have access to quelling strikes so that reduces their aggro, white mages have shroud of saints and such(yes you can DPS on whm quite well really - I do it often when other healrs want to solo). Not familiar if any other DPSs have anything like it. So the aggro bar really isn't much of an indicator. Also higher gear/weapons can easily outdps you. And simply some jobs are much easier to keep 100% uptime or output so much DPS that it takes a while.

If by melee you mean monk then it takes you a while to spool up your damage to greased lightining III at which point you should start gaining if not outdpsing most. For dragoon I'm not familiar with them but from my understanding they need a lot of positioning to get their rotation going and even one mistake can ruin that.