I think it all depends on your plan, room rate, budget, and not the least important-amount of people in your group. Having to move a group quickly, early in the am, after late arrival can be a challenge.
The last two visits I arrived at WDW after 12am. Ironically, I stayed onsite both times for my first night. CBR, CSR and it was so magical to just be there. The check in process went quicker, I was happy with my room assignment, and the staff can be relaxed and quite friendly at that time of night. We did have great rates at the hotels, so to stay off site may not have saved us much.
The few times I started our stay offsite we stayed at Homewood Suites, my husband wanted to know why we need to stay onsite after all the room we had, and the free very large breakfast buffet. LOL, He just doesn't feel the same about the resorts that I do. He did love the AKL when we went to check it out our last trip, I hope the next time we go together they have a great code there. I stayed at WL, after our first night at CRS(could not pass up the rate) and we loved it.
I think at the very least you should try a value or mod the first night if you don't want to spend so much for the deluxe. We had a car, but I understand that disney will transport your luggage if you are switching resorts.