Invisible Zippers come in 3 weights: #2, #4 & #6.
They also come on standard twill tape or mesh.
Twill tape is polyester & woven which makes it more sturdy.
Mesh tape (or YKK calls it Beulon) is nylon & knitted.
The size in your dress that just broke is probably a #2 woven.
Why did it break or pop? Chances are there was too much strain on the zipper. When zipping up an invisible zipper, the best way to do it is to hold the zipper together & then zip. You are taking the pressure off the zipper teeth.
As the size gets larger, the zipper is stronger. So if your zipper did pop & you need to replace it, replace with a #4 (medium weight invisible) or a #6 which is a heavy weight invisible zipper.
The type of tape does not make the zipper stronger or weaker. Twill tape is more sturdy & mesh tape works better with lace or where the zipper needs to flex.
NEW: At the bottom note that I stock REVERSE pulls (they look like invisible pulls) that can be applied to #3 & #5 standard coil zipper. If you have a bride that needs more strength in her zipper, this works!