Stayed at Doubletree Oct 30 - Nov 7 and used their transportation every day. Found it efficient and comfortable.
They pick you up and drop you off at parking spot #26 at each of the big four parks. This spot is only a couple of rows out in each parking lot, IMO not a long walk past where the Disney buses stop (and closer than where cars park) at EP, MGM, and AK. At BB bus had stop #1 very close to entrance.
Main difference from Disney buses is at MK. The bus stops (at spot #26 again) at the Transportation and Ticket centre, where you have to catch a monorail or ferry to MK (same as people who drive there do). Disney buses bypass the TTC and go directly to the park entrance. IMO, the monorail or ferry ride is part of the fun, especially for kids! We did both, and even managed to catch the right ferry for a great view of the fireworks as we were leaving one night.
Slow? I didn't think so. The buses were running, on time, to and from the 4 main parks every half hour while I was there. Less frequent to and from BB, so check the times. I've also seen complaints about Disney buses being slow, or about having to wait 45 min. or more for them. How often are Disney buses supposed to run, anyway? Had trouble finding out.
Doubletree shares buses with the other 6 DD Resort Hotels, which are all adjacent to each other on a strip within walking distance of Downtown Disney Marketplace. If your hotel is the first stop in the AM or last stop on the way back, I suppose it might seem slow having to stop at each other hotel. Doubletree seemed to be usually in the middle of the run. An 8:00 bus for MGM would arrive at Doubletree around 8:05, but an 8:00 MK bus might not arrive until 8:12 after stopping at some other hotels. Both buses would arrive at their parks by 8:30.
DD hotel buses do not run between parks, so we used Disney transport to hop around; eg. a direct bus from BB to EP and the monorail from EP to MK.
Disney cannot accomodate my family of 5 in a Value or Moderate resort. At Doubletree we got a whole suite for less than the price of a room at a Deluxe Disney resort.