Having a vasectomy is a lot less invasive than having one’s tubes tied.
I had mine 10 years ago and have had no side effects.
You’re in and out in about an hour, with some minor swelling and temporay discomfort.
But after that it’s clear sailing, so to speak.
Well, strictly speaking I would say that a vasectomy (barring complications) is “simpler” than a tubal. However, nobody I know who’s had a tubal had a particularly hard time with it. Nor do I know anyone who’s had a trouble vasectomy. So, I’d say it was a six-of-one, half-dozen-of-another call.
To tell you the truth, I’m not sure that my husband and I made the correct choice 15 years ago when he had his vasectomy. At the time, it was easier for him to have the procedure. He went to work for half a day on Friday, had himself snipped on Friday afternoon, relaxed over the weekend and was back at work on Monday. Because he was in the Navy the whole procedure was free – scheduling it on a Friday meant he didn’t even lose any leave. If I had had a tubal it would have meant a one-day hospital stay (at a cost then of about $9.00 – not much, but something versus the nothing we paid for the vasectomy). And, because I had just had a classic c-section when our daughter was born a few months before, my doctor would have required complete bed rest for a couple of days and no lifting for at least a week, maybe two. We had two babies at the time (our son is a little under a year older than our daughter) and so Kevin would have had to take a week or two of leave to stay home and take care of them, me and the house. In hindsight, we probably should have gone with the tubal. In our case, while Kevin doesn’t want any more children, I’m not supposed to have any more for health reasons. So, I probably should have been the one undergoing the procedure, since I’m the one who needed to be sterile. The fact is, Kevin preferred having his balls worked over with a crochet hook and a scalpel to staying home and doing my job for a fortnight, so that’s the call we made 
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Frankly it sounds like your wife feels more comfortable knowing that she’s sterile. Possibly this is because, as a woman, she’s used to being the one in charge of the birth control? Or maybe it’s just because, as the party who will bear the brunt of a failed procedure, she really wants to be extra, extra sure.
Jess
My guess with the surprise babies after vasectomies is that the man needs to have a couple sperm counts done afterwards to make sure he’s only shooting blanks. It takes a certain number of ejaculations to clear all the little swimmers out. If the guy doesn’t go in for follow-up, and the procedure WASN’T done correctly, the only way to tell may be with a little surprise down the road.
I’m getting an IUD next month, other IMHO thread about them notwithstanding. My SO refuses to get snipped and our insurance won’t cover a tubal ligation (but will cover a vasectomy, how’s that for screwed up?) and I want something long-term and non-hormonal. We already have 2 kids and that’s enough! 
I had my tubes tied during my second c-section when my son was born 20 years ago. I wanted to be the one sterilized because I was the one who had the pregnancies. At 35 I was really done with that! My marriage was shakey and didn’t last. I remarried and, although there was a brief period where my current husband and I considered whether we wanted to pursue a reversal, in the end we declined and have never regreted that decision. Don’t get bogged down in the “what if” mentality.