I use prewound for embroidery mostly, I have used it on regular sewing, didn't find much of a difference, do a break test to see how strong it is, thread has come a long way since I started sewing. The advantage to using bobbin thread is that you can get a lot more on your bobbin as it is a finer thread, there usually isn't the lint on it as well that some other threads have.
Ideally it is good to stick with the same machine but due to some circumstances that isn't always possible, like other have said, check to see that you are using the same seam allowance as that will make a huge difference in the size of the blocks
In my opinion there are very few hard and fast rules to quilting. Though some instructors have the way they do it and want you to follow what they do, whether it makes sense to you or not, or works for you or not, a good instructor should be leading you to learn ways that best work for you.