Some people like to generalize everything in favor of wives as if they are angels, while others do it in favor of husbands. If a woman marries a man, it does not automatically means that her/ his love is unconditional, because the situation varies from case to case depending upon their intentions.
My humble opinion is that the best way is to respect both mother and wife and give importance to the opinions of both of them. One should support the one whose reasoning is logical, BUT not in front of the other person, as in most clashes no one wants to be told that she is wrong.
The matter should be discussed while being "ALONE" in respective rooms of each of them. BUT it should be done with wisdom and sincerity so that non of them thinks that the man gives more importance to one over the other. He should humbly request his mother to treat his wife the way she would treat her own daughter, and he should request his wife to treat his mother the way she would treat her own mother.
In my case, the situation is totally different. Because my mother always give priority to my wife over me in every matter, while my wife gives priority to my mom over me in every matter. In fact, Alhamdulillah in one year they never argued or disagreed with each other in any matter but had a lot of combine disagreements with me. :( But that is a better situation for me then if it were the other way round. (Alhamdulillah)