It's not unreasonable to feel one is easier than the other - I find it goes back and forth for me depending on what's going on - but like others, I find the reasoning given odd.
Having cared for adults and children, and having had to be cared for myself as an adult, I find the "only thing that changes is that you ave an additional person to take care of" really dismissive. Caring for someone dependant on you takes a lot - there is no "only" there. Many find their goals and even sense of self has to be put aside to deal with the needs of caring. With most children, this level of caring is only a few years, but even as someone who wasn't the "main carer" when most of my kids were at that stage, I wouldn't call it "only" caring.
Yes, my identity changed when I had kids. Not only do my kids call me mum, so do random adults. "Are you mum?" has been a regular occurrence for me for almost 17 years now. I've never been asked "Are you wife?" Having eloped, there was a time when most people in my life didn't even know I was married, it went largely unnoticed unlike my having a baby. No one thought I was entirely different.
Even when I changed my entire name, no one really thought I was entirely different. I was just using a different name (though I'd been planning to change my whole name since I was small so few who knew me were surprised). My identity shifted less from a full name change than it did from having kids.
I find what life has thrown at me outside of marriage and kids has changed my goals dreams and aspirations far more than either my marriage or my kids. I've just changed a lot in the years since. What my spouse and I planned before we got married, very little of that came true and practically none of that is because of my spouse.
Some women do compromise a lot in marriage, but that's not to do with marriage itself but the culture around it in some communities and homes where the expectation is the wife follows the husband's lead. Marriage doesn't have to be like that and really, I don't think people should get married if they haven't discussed and found their future ideals to be aligned even knowing those are likely to change with life circumstances. It's working through those issues that help lay down the foundations when those changes almost inevitably happen. Sadly, that's not always a choice.
I don't think you are seeing things differently. I think you are doing things differently.
This.
I get the idea that being a wife at times can be harder, as many others said - our adult relationships often gets the leftovers after caring for children and work and everything when having responsibilities towards anyone else can feel like a drain.
Generally I find I'm happier when I spend more energy towards my spouse and our marriage - it's just hard to have it sometimes. I don't feel I've lost anything in my marriage, I've gained an entire different life I wouldn't have had otherwise. While I'm also happier when I spent more time with my kids, I can't say the same thing about having not lost anything - my body was altered and the pregnancies caused health issues and far more of my frustration in life is down to worrying about my kids.