The age old question here on the DIS! I've done both. When our budget allowed later in life we started staying onsite and we loved EMH every morning and the convenience of the short walk. Before we could afford to stay onsite we stayed offsite and still had a great time at DL and kept going back. When staying offsite we preferred hotels that provided breakfast, it just made mornings easier, but when they didn't do that we would bring breakfast items to our hotel with us (cereal, juice boxes) to get us going quick in the mornings.
I come down to these three questions for you:
1) Is it really busy when you want to go (ie school holidays) & will you actually get up early enough to do EMH?
2) Will you have to give up other things you wanted to do on your trip to accommodate it? (character dining, blue bayou, etc.)
3) How important is the bubble feeling? (stay onsite, charge everything to the room key, have packages delivered, park the car when you get there and forget about it till you leave)