Our family definitely prefers off-site, but it's a very personal decision. If possible, I recommend trying both at least once to form your own decision.
Onsite is better if:
You're a family of 4 or less
You go rope-drop to fireworks
You do well as a group in a fairly small area
You like to utilize Disney Dining (either the
DDP or just enjoy the restaurants)
You use the room basically to sleep and shower
You don't mind sharing a bathroom with the entire group
It can be better if you fly and use DME/Disney transportation
Offsite is better if:
You like space
You value out-of-park time
You want to visit other venues (Universal, Seaworld, Gatorland, etc.)
You have a group of 5 or more
You drive to WDW (and therefore, already have a car)
Don't mind buying or preparing simple meals
We're a family of 6, so there's definite cost savings with off-site, but it's more than that for us. We value our space. We like the multiple bathrooms, the private pool, the fridge full of snacks. OTOH, on-site gives you the Disney bubble--all Disney, all the time, that some people really appreciate.
Where you have a total of 16 guests, it might be worthwhile to rent 2 houses--if you look around, you can probably get two adjacent ones. Or a really big one, like the 6BR a PP mentioned.
It's also worthwhile for you to look at a DVC rental (again, you'd need more than one unit), or possibly Bonnet Creek (same). I've never stayed at Bonnet Creek, but I've heard good things, and the resort looks lovely.