Here's a few that I can think of:
Active:
~Generally more efficient on power
~No amp racks, saves space onstage and in the trailer
~Don't need speaker cables
~As many mixes as you've got speakers, as long as you've got the sends
~Most have a built-in LP or HP crossover, which can be handy sometimes
~Some have built-in mixers, which work for small stuff
~Preset delay and crossover points, some have a preset EQ curve to correct frequency response
~Built in limiters
~Can be easier to power than large amp racks when there's not adequate power
Passive:
~Possibility for better biamping/triamping
~Easy to add more cabinets on the same amps
~Ability to run several cabinets on one amp channel
~Only one cable to each cabinet
~Can save cable with multiconductor speaker cables (NL8 into triamped mains, NL4 out from mains to sub)
~Usually easier to deal with equipment failure
~No IEC cables to slip out of the cabinet during the show
~Locking connectors (ie- Speakon)
That said, I think that active systems are great for small-ish setups, maybe up to 3 mains/subs per side. Anything more than that, and you're better off going passive. Unless you've got something like a Milo rig (or something else by Meyer), or a powered Vertec system, or something similar, but that's a little different. One of the biggest advantages of active systems, for me, is the ability to be able to make do with less power than a similarly sized passive system. It can be a pain to run two cables to each cabinet though, especially when there's lots of cabs. Built in limiters great, they help to keep you from blowing things up.
In my experience, powered cabs aren't significantly heavier than similar passive cabs (maybe 20%), but the total weight of a passive system is much less without those amp racks.