I don't know that it is different. With the exception of some of the category of "feckless fathers" who have always sort of compartmentalised or shut off from their children, even when they lived together, my experience through friends/relatives/people online is that dads are just as devastated to lose contact with their children, but they accept it because they feel they don't have a choice. If they want out of the relationship, they can't force her to leave her children, and if she wants out of the relationship, he doesn't usually get a choice to take them. They may have got to a very dark place before they choose to leave the relationship - because really for a man who doesn't feel he can ask his partner to leave, he's talking about walking away from the family, not just the relationship.
In our current and past society, most adult men have been taught that men shouldn't show emotions other than anger, meaning that grief, loss, depression etc may come out as anger/aggression, sometimes extreme anger which eclipses common sense and a wish to do what's best for the children, it becomes a wish to hurt/punish their ExW. Contrastingly, most adult women have been taught that anger isn't ladylike and only other emotions are acceptable, meaning many many women turn anger inwards and blame themselves, leading to depression, anxiety, low self esteem, etc.
Or if this doesn't happen, still, many men lack coping mechanisms for their emotions due to their upbringing leading to responses like using addictive substances as a crutch, distancing themselves from the children because it hurts too much to see them and have to say goodbye at the end of the weekend or the 4 hours or whatever it is, or immersing themselves in things other than their children the rest of the time as a distraction which can become overwhelming and bleed into their time with the children.
I hope that these emotional difficulties will be lessened in future generations as we now realise the importance of letting boys be in touch with their emotions, but of course there are still parents who believe that "boys don't cry".
Secondly, I have gone through tough times with DS. At the worst parts I thought that if he was a dog, it would have been kinder for me to rehome him. Because he was (is!) a child, it just wasn't an option, but in those darkest times I did think that if I knew it would cause him no long lasting distress and he would be absolutely fine, I might have done. That terrifies me now, but I never came close to actually doing it, and the reason why was that I knew on some level that even if I felt like a crap mum, even if I was finding it hard to spend time with him, he would still be devastated if I left, it would still damage him, he still needed me to be there however crap I was being or feeling. And on a very basic level, yes he probably would have been fine with just DH but I couldn't bring myself to do it. I don't think that's a female thing, it's just a logic thing - logic won out over what I felt I wanted at the time. I suppose I just wanted to say that even if you ever did experience feelings like that, experiencing them is no reason to act on them, there are a lot of barriers in your way (as a woman especially) to doing it. Now I am horrified that I ever thought, even hypothetically, about giving him up and couldn't imagine it.
I don't think men and women are fundamentally different, I just think we grew up in different worlds, and it's still the case now.