There is no answer to this because of wildly varying situations available on both sides.
I've done both. Being a SAHP is a totally different kind of hard. You dont have targets, appraisals, fear of being fired, expectation to be dressed/made up a certain way, arsehole colleagues/clients, childcare worries... the list is endless.
What you do have is boredom, monotony, no definition between start and end of work, no solo walk in to town on your lunchbreak or lunch with friends, no quite coffee break. Also the worry of only one income can be crushing.
Your children see you as default parent so even when your partner is home it's you who does the work. In my experience anyway.
I had a cleaner through both roles which helped massively.
The only thing I can't see as an argument is that sahp parents of school age children can possibly find it as hard work as working parents.
Assuming the kids don't have SEN, what can be hard about 6 hours to yourself every day??