When I was married to my son's father, we butted heads quite a bit about how to raise our son, deal with his behavioral issues, etc. I subscribed to the "attachment parenting" philosophy, while he wanted to go a more traditional route.
The compromise my ex-husband came up with was that I would raise our son until he was 13, and then he would take over. I agreed, knowing that this was a ridiculous idea, but it gave me free reign to raise my son as I saw fit.
Ten years later, my son is an amazing, funny and wonderful boy. He still has some behavioral issues, but for the most part, he's a delight. Despite the warnings that co-sleeping, paying attention to his needs and being respectful of his feelings would make him a spoiled brat, it turns out that just the opposite is true.
My story, however, is probably unusual.
Here are my thoughts for what others might do in this situation:
1. Write out your parenting philosophy/ies, trying to be as specific as possible (for this behavior, I'd use "x" method).
2. Come together and present to each other what you have written.
3. For each behavior, discuss why one method might be better than another for YOUR child/children, keeping in mind that every child has his/her own personality and ways of doing things. Some methods will be more productive than others.
4. Try to find common ground.
5. If you can't come to a compromise during the discussion, perhaps you could target specific problematic behaviors (such as whining) and try both methods of dealing with it. See if one works better than the other or if perhaps a combination of methods is more effective.
6. If all else fails, find a parenting class you can both attend. Sometimes a third party can help suggest ways of raising your child that neither of you thought of.
It is important to present a united front if at all possible. Children need consistency. Raising a child is trial and error sometimes. They don't come with manuals, unfortunately, so you and your spouse will have to write your own. :)