In the past we stayed off-site and very much enjoyed it. Granted, we were younger then and had more patience and energy - awwww, early 20's, THOSE were the days!
Now, we're in our mid-.......40's

..... and we have 2 children (13 years old and 4 years old). We stay on-site.
Quite frankly, I think both options have great benefits and both have some negatives. When we stayed off-site, we found some fantastic deals on large rooms (I love Embassy Suites!), which also cut down our food costs (large breakfast included with room). We drove to the parks and stayed for the day. We also took advantage of off-site dining which we don't do anymore, and shopping at some of the outlet malls nearby. Thinking back I have absolutely no regrets at staying off-site then. It was great!
Once we started having kids, though, it changed. For us. We wanted the option of using Disney transport anytime we needed it for naps, extra hot days or just if the little ones didn't sleep well the night before and we needed extra breaks during the day. It's so much quicker to hop a bus and ride back to an on-site resort for naps, breaks, etc. rather than trundling out to the car and fighting traffic to a hotel off-site. Plus, we were much more likely to go back for fireworks, parades, etc., than if we knew we were going through the traffic and parking lot ritual twice a day. So, we no longer rent a car (gotta love magical express!), and eat all of our meals on-site.
I don't think there are any "right" or "wrong" ways of doing Disney. Whatever suits you best, be it financially, time-wise or preference, is what you should do. Would I recommend trying both if you can to compare for yourself? Sure! What have you got to lose and you gain a great vacation either way.