If I may say, alongside all of the actual advice most people can give you along with the links to FFXIclopedia for DRG and NIN... the best thing to consider when doing any job is your personal style of play (i.e. mindset, strategies, budgeting, etc etc).
All in all, though..
NIN is a good tank against most enemies that hit hard and slow. If you gear yourself correctly, you can also do decent damage while you are at it. NIN was created to be a damage dealing job, with survivability using Utsusemi and Evasion. However, it can be used (now) for tanking, damage dealing, or a combination of both with some good balancing. Overall, I'd say NIN is good if you have the money and the patience to learn the mechanics and timing of things.
DRG is essentially a damage dealer, plain and simple. Yes, as a result, you will end up having slow invites due to so many DD jobs (both physical and magical). However, you can decently solo with the job using /WHM or /BLU, having a good strategy, and knowing your limits. DRG's Jump series abilities are wonderous for dealing damage and shedding hate. I personally tend to use Jump as soon as it is active during a fight, while saving High Jump and Super Jump for after using a weapon skill (typically due to hate-nabbing numbers). I switch back and forth between the two, though try to use High Jump first if it's up (and obviously, if that isn't good to shed enough hate even though it typically is, I'll wait a bit to see what happens and might Super Jump). Anyway! With some patience and some time to get decent gear, you can easily have a well-balanced set of equipment for DRG. It's not too expensive if you do things right, too. And you can still deal good damage on a budget with DRG! Good strategic use of WSs and abilities is a plus, too (see above with High/Super Jump and high-damage WSs; along with using WSs like Leg Sweep to stun long-delay monster abilities or for interrupting enemy spells). Overall, if you like some versatility in play style and have some patience, you might enjoy DRG as a straight-forward damage dealer / semi-solo job.
This is just my personal insight of the matter - just remember, that it is YOUR style of play that determines whether or not the job is meant for you. Plus it's really what determines the pros and cons of the job - any problem can be dealt with by thinking up a nice little solution for it that fits you best. ^-^