I have used the Airport Valet for years with no issues. It can be a challenge on occasion when they are located a good distance from your gate but otherwise a solid service.
You should always avoid using FreedomPark DFW valet. These guys are the red-shirt valets that meet you and take your car offsite.
The first time I used them, FreedomPark DFW valet left my car electronics in an odd configuration that spoke to their lack of understanding. I complained and they promised to make changes. FreedomPark DFW then offered me a complimentary service for the next trip. There were no issues.
Then the next trip, FreedomPark DFW returned my car with every warning light on. The car was in safe mode. The driver was upset and crying saying she didn't expect the car to roll backwards and did something to the shift lever then the lights came on... I took the car to BMW that day, it cost me $3K and FreedomPark DFW valet president, Ken Kundmueller wouldn't even take my calls. They were too busy calling my BMW service writer asking him to prove they did something wrong then denying to me that they called BMW.
They kept avoiding me when I asked them to do something. His son John Kundmueller would text then email saying they didn't do anything.
Don't risk your ride with these guys. This company is two kids running daddy's business. Very bush-league.