I have never used EMH. We can't get up early enough for AM EMH and with little kids, we have no interest in late night EMH. But staying on property is TOTALLY worth the $$$.
First of all, the off-site hotels I'd want to stay at aren't really that much cheaper than WDW. I actually booked the Doubletree in DTD with a Mousesavers deal for May and it definitely was lower cost, I think about $850 including tax compared to the $1500 for AoA. However, if I did Doubletree, the shuttle isn't NEARLY as good as WDW shuttles. I'd have to rent a car (at least $300 for the week for a car big enough to fit my family) and I'd have to worry about carseats, I'd have to pay for parking at WDW ($14 x 6), I'd lose out on the Magical Express luggage service and I'd have to haul my 3 kids and all the luggage to pick up the rental car. Not to mention, after a long day at the park, I'd have to remember where I parked that rental car and sit in a HOT rental car with the kids. I'd eat on-site just as much because, lets face it, I'm usually in the parks at meal times. And really, the food at WDW isn't THAT much more expensive than regular restaurants. I don't really eat at cheap restaurants at home. And that's just practical stuff. I like the Disney bubble, the Disney customer service. I like that the hotels are themed and not generic hotels. Oh, and that Doubletree? It may be cheaper, but the rooms only have one bathroom. There isn't a real door between the bedroom and the sofa. And I have to pay an extra $10 a day for a bed for my toddler. Once you add that all together, the cost difference narrows quite a bit and suddenly staying on-site isn't THAT much of a premium.