I have tried LOTS of monofilaments. Not in the bobbin though, I only use regular thread in the bobbin.

In my trials, the most invisible is YLI but it is SO thin I find it hard to work with so I only use it on very small projects. Gutterman has had the least breakage for me, but it's thicker and not nearly as invisible as the YLI. The Sulky at Joann did not work well for me, lots of breakage. But that may be due to me or my machine (Babylock) as I know lots of people like Sulky.