Agreed, my wife and I are perfect examples of your comment. My wife was tightly controlled at home, and consequently went nuts her during her 1st year of college away from home. I won't go into details, however, think of everything you can imagine, and you won't be far off.
OTH, I was allowed to have enough rope to hang myself with. Guess what? I never did.
So which parenting styles do we have? Unfortunately, my wife is STILL on board with the Iron fist approach, while I have adopted the rope approach.
With my kids the rope approach works better, and has led to greater trust. They'll tell me stuff they'd never tell Mom about.
As you've written, it isn't necessary for parents to have an identical parenting style. Also, not every kid requires the same treatment either. Some kids will take all the rope you can give them, and some won't. I am sure on some things some of your kids don't worry you as much as on others; what is a problem for one isn't for another.
Some kids may need to be under an iron-fist method. As for your relationships with your kids compared to your wife, I've noticed that kids tend to talk to one parent more than another - usually the one they feel more comfortable around. But also sometimes the one they think will be more lenient, especially when they're asking for something they're pretty sure the other parent would shoot down. You have seen your kids try to play you against mom, hmm?