There is a lot of confusion about the current state of the kennels on Disney property. They have facilities at TTC, Fort Wilderness and Epcot where the staff will walk and feed your pet for you. The only kennels that do not provide that service are Studios and AK. (Side note: ALL the kennels on property require proof of vaccinations in order to board your pet...which the owner should have anyway if they're flying with their pet or driving across state lines with their pet in the car. At least if they want to do it legally...) Most people end up being confused because if you don't make a reservation ahead of time, chances are the only space available will be at Studios or AK where you will have to return to walk and feed your own pet, which leads people to believe that these services aren't offered at any of the kennels. (Another side note: I've never understood why someone with a 100 lb. Great Dane would travel all the way to FL with their dog and not even call first to see if they are going to have space to board him.)
The facility at Epcot is the largest and also one of the most popular. They are almost always full for dogs over 50 pounds. Same goes for the one at TTC, although they are a bit smaller. The one at Fort Wilderness is almost always full...period. They are the smallest kennel and have returning customers who vacation every year at FW that bring their pets every time. Doesn't matter what size dog you have, if you show up unannounced, you'll most likely be turned away.
The kennels at Studios and AK are hit and miss. They are both fairly large facilities (AK being larger than DHS) and get full for dogs over 50 pounds quickly because they are the only option when the other three have to turn people away. During holiday weekends and busy times, these kennels get completely full as well. During non-peak times, these kennels can be like a ghost town. Some people choose to board there because they don't want strangers handling their dog, others are forced (unhappily) into the situation and even though they're told they need to come back to walk and feed their own pet and sign paperwork agreeing to do this, they will not return long periods of time to take care of their pets. They assume the staff will just take care of it but at AK and DHS, they will not. The new center will be good in that respect, because all the animals will be taken care of by the staff.
If I had to guess, I would say that they have room for about 50 dogs over 50 pounds between all 5 kennels, a lot more than that for dogs between 10 and 50 pounds (probably close to 150, if not more) and a bunch of spaces for dogs under 10 pounds, which hardly ever fill up. Sounds like they're cutting back on the space for cats at the new center though.
With all that being said, the company that took over is a nationwide company however the kennels on Disney property are their only locations in Florida. Draw your own conclusions from your own experience (and things might be handled differently at the new center) but in my experience, an isolated operation with inexperienced employees away from the eyes of upper management and corporate is rarely a shining example of how the business should be run.
And this goes without saying, I'm sure, but it is against the law to leave your animal in a parked car in FL. If Security sees an animal in the car, they will get Orange County to break your window (fastest method) and remove the pet. And then press charges...