I've used DME three times, and it's been fantastic each time.
The first time, we got off the plane around 9:30 a.m., got to our resort by around 10:30 a.m. We had our immediate needs in our carry-ons. We were lucky in that our room was ready so early. We rested, then got lunch, explored the resort, went swimming, and when we returned from the pool our bags were in our room. Since we weren't there, we don't know exactly how long it took, but we were out of the room starting around 2 hours after check-in and returned about 4 hours after check-in, so the bags came some time in that time-frame.
The second time, we got off the plane around 10 p.m., got to our resort around 11 p.m. I forgot to ask to have our bags held 'til morning (again, we had well-stocked carry-ons), and our phone rang at 1:16 a.m. saying our bags were ready if we wanted them. So our bags were ready for us 2.25 hours after check-in.
The third time, we got off the plane around 8:45 a.m., got to our resort around 9:45 a.m. Our room wasn't ready until 5:15 p.m., so I honestly can't say how long it took for our bags to arrive, since they would've had to stay in the resort's storage until our room was ready.
Overall, what I can tell you from being on this and other message boards since DME began nearly 4 years ago is that DME works as promised. Are there exceptions? Of course! But they are exceptions, not normal occurrences.
I can also tell you that DME uses a high-tech system to track the luggage. Each DME luggage tag has a barcode. The barcode is scanned 5 times during the entire process in the Orlando area, from airport to resort room. And the luggage delivery trucks are tracked by GPS. In other words, Disney knows where your bags are at all times.
If you do choose to get your own bags at baggage claim (leaving the DME tags off your bags, of course), please realize it is very very likely that you will delay your own arrival at your resort. In the time it takes you to go to and wait at baggage for your bags, it is highly likely that you will miss the next available bus to your resort and will have to wait for the next one.
Whatever you decide, you'll have a great time during your stay!