I just think that if the worst kind of tragedy were to happen like if all your kids died in a car accident you might want to make another. People think they'll be together forever but in reality divorce is pretty common.
If both of you agree that this is the final kid, the vasectomy is the easiest from all options. You don't want her to use birthcontrol for the rest of her life and fill herself with disrupting hormones.
And it let's you return the favor after your wife wrecked her body with those 4 pregnancies...
There are a few studies that have shown little (not out of the normal range of variation) or no effect on hormone levels after vasectomy. Also, often they go back to the previous levels after some time. Based on all that, I'd say that, compared to the effect of oral contraceptives, vasectomy seems to have a very much significantly smaller effect.