I personally love my Dr. Cook's, and my mare does as well! When I first bought her, she was incredibly sensitive to the bit. She would back up dramatically when bridling, toss her head around, and refused even the slightest contact. She now happily drops her head into her bridle, and accepts contact with ease! I have ridden with a bit all my life, but her obvious discomfort with the bit really pushed me to find an option that worked for her.
I think with bitless, it is really about trying out what is right for you and your horse. My mare has taken to her cross-under Dr. Cook's really well, but many have said it causes their horses to lift their heads, it does not allow a quick enough release, etc. There is no "best" bitless bridle...the best one will be what your horse prefers and what allows you to feel safe and like you are able to effectively communicate with him. You may have to try a couple different styles to see which one is the right fit.
There is a style we have here in Canada called the "Nurtural" which you can Google. Not sure where you live, but it is a cross-under style with a piece that helps with the release issues that some have with the Dr. Cook's. There may be something similar for you to check out wherever you live as an option. I have also heard positive responses to using the Micklem style bridles in their sidepull setting.
No matter what, listen to your horse, and don't give up on bitless if one type doesn't end up working. It might be a process, but I think it is really worth it in the end. You know your horse better than anyone, so if you are feeling he would do well in a bitless, then it will be well worth the effort to find him the right fit:)