I ride both mine in Dr Cooks. 13 year old used to be considered 'really strong' and had a Pelham, which he fought. He is a lamb in his Dr Cook. 5 year old, broken this year, absolutely loves his.
In answer to your question , No it doesn't mke them more difficult to control. With my two, taking the bit out their mouths allowed them to concentrate on what we were doing and not be constantly bothered by the 'noise' going on in their mouths. I can stop both my horses using voice and seat aids, without touching the reins and one has only been broken seven months.
Not all horses get on with them, not all riders get on with them. They don't suit everyone's needs and are certainly not a panacea for all ills. I have used mine on three other horses belonging to friends as I don't like riding with a bit (I spend all my time worrying about being heavy handed and not actually riding) and had no problems even with one described as 'gasolina' ie very excitable.
i've used hackamores on and off for years. i bought a nurtural (like a Dr Cooks but with stabilising circle under jaw) last year and use that occasionally.
i think like every other bit of kit, there are horses that will love them, and horses that won't... and they'll suit some people's riding, and not others.
I use a Dr Cook on one of my girls for show jumping and it's like riding a different horse. she used to just fight with a bit - mild or strong - whereas with the dr cook she's responsive and doesn't fight. i can let her just run and jump. i'm lucky though that she's really careful, looks for her fences and loves to jump. not sure that i'd want to ride everything in it, but it works for her!
I used to ride my tb in one of these and for a while it really relaxed him ( he had undiagnosed kissing spine at the time). I have used it on my irish cob who had no breaks in it or stearing, and have ridden a 17.3hh warmblood in it who was so soft and responsive in it once he figured that he didnt need some one hanging on to his mouth to work on a nice out line.
Some people don't agree that dr cooks release quickly or effectively to relieve pressure quickly however I used the english leather one and and felt I had no problems. So not sure if this has an effect?? I have also found cheaper copys are not designed in the same way. I can remember how not as I have sold my dr cooks on however I do remember that the cross underneath the jaw flowed as one piece of leather from the head band and the cheaper versions did not. However its the same with treeless saddles some horses and riders really get on with them and others don't