It’s difficult to gauge the depth of any person’s emotions in comparison with another person, so I don’t think there’s a way to definitively answer your question.
But I happen to have a relatively unique experience in that I’ve lived part of my life trying to uphold the lessons I learned about what it means to be a man, and now am living as the woman I have long felt and known myself to be. So here’s what I can offer to try to answer your question:
Society teaches men that they must be in control of their emotions at all times except for certain specific circumstances which make it socially acceptable to show a few more emotions – death of a loved one, exceedingly good news, winning a major battle, etc. Men are taught to never cry, to never show sadness, to be stoic and stable. Men are largely told to only feel anger, happiness, or some form of being amused.
On the other hand, women are granted more latitude with emotions; it is socially acceptable for a woman to cry (but it often makes men uncomfortable for a woman to cry in front of them), to be silly, to be sad — to be more expressive of what they are feeling.
So it may not be that women experience emotions more deeply, but it is more socially acceptable for them to express the emotions they feel.
One more difference I will point out is that before I began taking estrogen, my emotions felt dulled and somewhat inaccessible to me. Once I began taking estrogen (and dropping my testosterone levels), I felt those emotions become more present, more accessible, more vibrant. It’s kinda like in the movie The Wizard of Oz, when Dorothy is in Kansas, everything was black and white – kinda dull. When she opens the door to her house in Munchkinland, the colors are bright, rich, varied, alive!
I’ve heard from some trans men that their experience was that their emotions were overwhelming until they began taking testosterone, which seemed to bring the emotions under control for them. But they did not indicate that they lost any depth of emotion, they just had more control.
So perhaps hormones play a role in the perception of accessibility of a person’s emotions, but it would be a bit of an overreach to suppose that hormones grant or take away depth.