First and foremost, lies the keyword in the description: irreversible. There are circumstances and procedural variations that result in them being reversible, but for the most part, they're called “permanent” birth control for a very good reason. The two most common procedures for this, tubal ligation for women and vasectomy for men, are both done surgically. These methods are not particularly invasive, but they often require cutting certain tubes in the body. The tubes differ in both males and females, but the basic concept is to prevent the sperm or egg cells from reaching their respective destinations in the body, thus cutting off the possibility of conception. These procedures are permanent and irreversible, so unless a person is absolutely certain they do not wish to have children, then this option should not be considered.
There are also potential consequences to both procedures outside of the realm of birth control. While the statistics have varied on both counts for both genders, there are reports that both tubal ligation and vasectomy can have an effect on female and male libido, respectively. In theory, this should not be the case, because neither procedure is known to have an effect on hormonal levels or anything that might have a physiological effect on a person's sex drive. The effect, conforming to expectations, is a negative one, though most statistics that do show a decline (most report no noticeable change) reflect only a slight adjustment, with only extreme circumstances showing a decline of over 10%. Still, it should be noted that these statistics are highly subjective, and what is only a slight decline in some might constitute a complete loss of libido in others.
One final consideration should be which one of the couple gets the procedure. Both forms are invasive and may pose complications. Also, there might be some personal objections that have to be considered. This sort of thing can be very subjective and not all objections are going to be firmly in the realm of the medical and the reasonable. While some might describe apprehensions to getting tubal ligation or vasectomy to be irrational fears, it should be recalled that what is defined as “irrational” to some might prove to be perfectly reasonable for the person making the argument.
Once all considerations have been weighed, then the only thing left is to consult a medical professional on the matter. Yes, the procedure is permanent, but there are ways to make sure that there are ways for a couple to conceive a child even after the “snipping.” For example, it is now possible to flash-freeze sperm, making sure that the couple can still use artificial insemination. Also, a medical professional is going to have better knowledge on whether or not a reversible procedure is advisable, given a couple's specific circumstances.