I don't know that any service is faster than others since they should all be very quick. Ease of use and the process are different obviously.
Drone Zone does not provide LAANC clearance at all. I have not used Kitty Hawk.
My preferred method is Skyward whenever I have time to plan and submit in advance. it is well laid out and you get a nice printout of the clearance that lists all of the details. I take it with me so that I have the information in case I get approached by anyone.
If I need to get cleareance in the field then AirMap is my choice. It does the job and is fairly easy. I have run into times when AirMap just won't work right with LAANC and that's why I always prefer to get it in advance with Skyward.
do you ever just not receive one? It has happened to me a few times in last month for places i always got them in 10 seconds but its random not persistent.