The injection can save you life if you are heavily bleeding but most people who get the injection do it because simply because it speeds things up, which the doctors tend to be all for too, so unless there is a medical reason it's mostly just for convenience.
A few people have an allergic reaction to the synthetic hormone used, this is rare but because I've had allergic reactions to quite a few drugs in the past I'm opting for avoiding any drugs that are not essential. As someone mentioned many sources say that it can interfere with your natural hormones that help with breastfeeding.
The injection helps to cut down on blood loss just after the birth, but I've also read that it slightly increases the risk of hemorrhage in the days after the birth because it speeds things up so much sometimes part of the placenta breaks off and stays behind, causing complications later. This can happen at any birth but apparently is less likely when the placenta is left to deliver naturally.
There are advantages and disadvantages either way, unless there is a medical emergency it comes down to which way you like the idea of better.
