In Justice League: Crisis on Two Earths, it shows this world has the alternate versions of Wonder Woman and Batman together as a couple. It makes you question if this implies that the real Bruce and Diana are compatible.
On one hand, the immediate answer is no because this is the opposite dimension. They're together in the bad one, so they shouldn't be in the good one.
But on the other hand, you have to examine why these two work well as a couple.
Superwoman is a vindictive, domineering, and promiscuous brute who values Owlman's drive and passion. She immediately drops her ambitions at the prospect of something greater. Owlman is a complete nihilist who is souly driven by his mission to find purpose. They're down to have a little fun before it all goes down. Their craziness compliments each other.
Now examine Diana and Bruce. Wonder Woman is a selfless, supportive, strong-willed agent of peace and love who will stand for anything as long as she believes it's right.
As Owlman's opposite, Batman is the most caring person there is. He does what he does because he belives there is value in every life. His purpose is defined by his mission to preserve all of that. Bruce and Diana's VIRTUES compliment each other.
Therefore, I believe that WonderBat is a good ship on a fundamental level.
