I was wrong to use the word "obviously", and would change it to "in my opinion" if I could still edit that post. And definitely did not intend to minimize mens problems - I'm a man myself and have first hand experience. I've had this conversation with a friend who is a outspoken feminist who I felt erased the problems men faced.
I don't have time to show my thoughts with any objective metrics, so I'm just going to lay out how I see things, so this will be touchy-feely. This is merely my opinion and I have no problem with people disagreeing.
I think the biggest impact is in how people can function in modern society - pay gap, positions of power, tokenization - a good book is "Invisible Man" by Ralph Waldo Ellison which is about more than being black in America but about being an individual that everyone wants to put in a box or a particular group - he's invisible because people don't see the individual. It's universal, and everyone feels that to some degree, but the degree I feel it as a white male is much smaller. Basically your ability to project your will on the world is easy mode for white male (btw - me).
Anecdote alert: For example I was literally just talking to an old friend who I've worked with in the past who is a great architect but kept getting the in-the-middle-of-nowhere projects at a very well known and old NYC firm, so she started her own architecture business and is doing quite well.
But not that it makes things easy for men! Because there is also expectation to be a provider, suck up your emotions and be tough. These things, which some point to as "the problem" are harming men as well and should be addressed. And this is where it gets very messy - some of the things that are "evidence" that men are privileged are also things that harm men in non-obvious ways. And as for the "easy to project your will", there is also an expectation that you have to and you're a failure if you don't. Why can't someone live a simple life without feeling like a failure?
Ultimately I think the ideal goal should be to not push gender based expectations - both for male and female.