As someone who was sterilised many years ago, can I give you my take on it?
The fact is that when contraception fails it is the woman who has to carry the can (so to speak!), and all the cries of "It's not fair" and "He should take some responsibility now" make no difference to that fact.
If you get pregnant, you could end up, through various events, to having to have an operation, sedation, whatever.
The sedation for sterilisation is light, unlike a full anaesthetic for a major op. I was home within 2 hours, and right as rain the next day.
The sense of liberation from having to worry every month for the next 20-odd years was fantastic, and I never suffered any ill-effects at all. Contraception became completely irrelevant.
The other consideration was that i KNEW that even if something awful happened to DH I would never want any more children, whereas if something happened to me I couldn't bear the thought that he would be denied the opportunity to have more children if he had a vasectomy.
That coupled with hearing the problems his own father had after the snip made it a complete no-brainer for me. And I say for me, because as far as DH was concerned the decision was all mine, for the pregnancy-related reasons above.
Please give it some consideration, and you'll never have to worry again.