While both procedures might seem similar to the layman, they are very different. Tubal ligation is a much more complex procedure, and has its fair share of risks as well. The patient will have to undergo an epidural or general anaesthesia and the procedure takes much longer than a vasectomy. It also has a much higher risk of complication.
As you can see, vasectomies aren’t that scary after all. If you still have questions, we strongly suggest you talk with a professional