I've used them many times....good service.
Advantages??? Quicker, nicer.
Disadvantages?? Cost a ton more. You should take your bags with you.
It all depends on what type experience you want. If you want something more personal, go with TT. They will meet you at baggage claim, help you with your luggage and then off to WDW you go. Should take about an hour total...gate to resort. (30 min ride to the resort, 10 min from gate to baggage claim, 15 mins at baggage claim, 5 mins to walk to and get into the car...about).
I don't recommend tagging your bags with the DME luggage tags as some do. There is no way for DME to know if you have any missing bags, so you may not know about a missing bag for hours. Much better to just get them at baggage claim. Cost for TT should run about $115 (about) plus tip.
I also recommend packing your carryon bag with anything you may need to start your vacation in WDW...the airlines do misdirect bags all the time. You don't want your swimsuit in the bag that goes to Detroit!!!
If you take DME, it should take you about 70-75 mins. 15 mins from gate to DME area, 5 mins to checkin and head to bus lines, 10-15 mins in bus line, 10 min wait on the bus, 30 mins to resort. It could be as short as an hour or closer to 90 mins...but seems that 75 mins is about the average time to date.
With DME you can tag those checked bags and have DME move them for you. But, be sure to pack anything you may need in a carryon bag...you won't get your bags for up to 4 hrs after resort checkin...not DME checkin, but resort checkin.
I have used DME many times...and the vast majority of times the experience has been good. I have also used car services as well. It all depends on what I want for that particular trip.