I've done both and like both for different reasons.
Onsite -
Pros: Have the convenience of WDW transportation, don't have to rent a car/drive, have EMH hours, and are completely immersed in the Disney experience. Depending on when you go, you may get free dining.
Cons: You are 2 adults and 2 children in one small hotel room, you have to eat all your meals on-site, you have to wait for the buses, rooms are more expensive on-site than off.
Offsite (we rent a vacation home):
Pros: Much more room to spread out, own pool, full kitchen, washer, dryer, game room, etc., usually much less expensive than staying on-site (last time we rented a 5 bedroom/3 bath private pool home for $700/wk including all taxes and fees), we have our own car so we can eat whereever we want and aren't tied to the WDW bus schedule. We also save some money by eating some meals in. Also, with having your own car its easier to load and unload the kids/strollers. I like being able to get up in the morning, start the coffee, get my shower and get dressed before getting the kids up, having breakfast in the house and then getting to the parks. The kids also like having the pool all to themselves.
Cons: You have to rent a car which is an additional expense and pay to park. You don't have EMH.
As far as the driving time goes, unless you stay in a monorail resort, I've found I can drive from the rental house, park and get to the park gates in about the same time it takes to wait for the bus, get loaded and get to the gates. For me, I've also found that its just as easy to go back and forth to the rental house and the parks as it is to go to and from the resorts/parks.
Generally, if there are just two of us traveling we stay on-site. Anymore than that we stay off-site. There are three of us going in December and we opted to stay on-site as I got a free dining PIN. If it hadn't been for that we most likely would have rented a house again.