We've also enjoyed both and will likely return to both. They're different and either could be favored.
When we stay onsite, we like to camp at Fort Wilderness in a pop-up camper. In a hotel room, we prefer the deluxes for their wonderful pool areas and convenience to the parks. The moderates are nice too, but too small for our family of 5 (DH disliked DxL). AS are fine for sleeping or very young children, if one reeeeally wants onsite. Didn't care for them otherwise.
Offsite, we have had fabulous stays in 2-BR/2-bath luxury timeshare villas: Great pools, organized activities, screened balconies, full kitchen, inroom washer/dryer, spacious DR/LR, several TVs and king MBR suites with jacuzzi tubs... loads of comfort & privacy with kids! Who could ask for more?!?
Budget is really the issue, though, because Disney Vacation Club resorts offer the same thing... really beautiful, best-of-both villas onsite... at a premium that's beyond our means unless we wanted to limit our annual travel to about 5 nights/year. Since THAT's not happening, we spend most of our stays offsite in top notch digs (sometimes ending with a short, discounted, deluxe stay onsite) or onsite camping. If you spend most of your time at the parks, you'll have fun no matter where you stay, so long as it's fairly nearby! Enjoy!