We moved hospitals for the birth of our twins to find one that was willing to tie her tubes when they took the twins out. She ended up having to have a hysterectomy for other reasons later but them being willing to tie her tubes during the c-section was a big part of our decision on doctors to see.
My mom had a hell of a time getting her tubes tied after my brother was born. She had to argue with the doctor for a while to eventually get it done. Gave her the old “What if you change your mind later?” line in like 5 different variations. The one that really angered me though when she told me the story was “What if something happens to one of your children?” Like you were just replacing a busted TV or something.
Generally yes vasectomy is safer. But if they’re planning to give birth via c-section for whatever reason for example, then in practical terms there’s basically no additional risk. Plus neither method is totally effective. So if you can both get fixed you have much better chances of not getting pregnant accidentally.