The main advantages are hard to explain because not everyone cares about the same things. For me, the hotel experience is very important. No matter how much people rave about their favorite Harbor motels, there is not one of them that comes close to what you get at a DLR hotel. They simply can't afford to offer acres of landscaped grounds, gazebos, restaurants, shopping, activities, etc etc. They don't have marble, granite, or even real glass instead of plastic in most of them. They don't have luxury bath supplies, characters in the lobby, topiary Disney shrubs, a giant lit Sorcerer's hat, *character meals, private park entrances, discounts on taxis, package delivery to the hotel, early entry for every single day of your stay, DTD steps away, the monorail next door, etc etc. At the resort hotels there are *spas, waterslides, pools & hot tubs, *onsite childcare, special activities for guests, and entertainment, rooms that often have a lot of Disney magic (music and fireworks in the headboard, for instance!) and a sense of being in the heart of Disney.
*these items have a fee
It's not cheap to offer all of that. It isn't cheap to maintain and refurbish the way Disney does. The prices of the hotels reflect the fact that it costs a lot more to give guests a resort experience than a motel and also that the demand is high enough to set a higher price. The nice thing is that at DLR, you have the option to choose to pay to stay at the resort or save your money for other things and still enjoy the parks. It's not a bad idea at all to mix it up and stay onsite once (or once in a while) and offsite at other times.
Most of the time, I stay onsite. There is nothing like it for me. However, I go often and my agenda is broader than hitting the parks non-stop. I love to enjoy the lounge at GCH, shop in DTD, lounge by the pool, etc. I love having a retreat to go to during the day and return to at night.
For me, the hotel is not just a place to sleep but an integral part of my DLR experience, so I'm willing to pay more. I usually go when prices are lowest and discounts are offered. I use my AP for room and dining discounts when they are best, and in the past this has made my onsite stays only somewhat higher than offsite prices. That is probably not going to be true this year, as it seems that prices will be higher with the opening of CL and the DLH refurb. Still, if you watch for deals you can usually swing an onsite stay for a decent price.
One last piece of information about this is the fact that I usually think of a DLR trip as about 2-4 nights. Longer stays can definitely add up.