Fonz and Porter had this question on their Saturday morning show a few years back. They said the thread is lighter, therefore you get a lot more on your bobbin. The only difference is: serger thread is two ply, while most sewing threads are three ply. They said you would be fine using the cones of serger thread.
The reason the serger thread broke on the knits, is that the needle threads in serging are straight and flat, and any thread is likely to break on knits that stretch. Try to give a tug on those pieces as they go through the serger and see if that helps.