I like to do invisible machine applique a la Harriet Hargrave and have always used YLI nylon monofilament for this purpose. Recently I bought some Invisafil thread in the color of the background fabric to try. The Invisafil thread itself is very nice, but my results with Invisafil were not as invisible as my results with YLI, so I will still be using YLI in my next project. I have also tried some invisible polyester threads (including the one from Superior) and found that they also are not quite as invisible as the YLI.
When I use YLI for invisible machine applique, I use a 60-wt cotton thread in the bobbin and loosen the top tension on my machine, adjusting the stitch so that the bobbin thread never shows. My YLI is on a large cone, so I place the cone in a jar behind my machine, place a serger thread cover on top of it so the monofilament feeds out of the top of the cone, and use an "outrigger" for threading (a flat stick with one end going over the machine's thread spool and a hole in the other end for the thread to feed through).
It really depends on how you want to use the Invisafil. If you are looking for something that will work for invisible machine applique (turned edges such as with freezer paper), then IMO Invisafil is not as good as YLI nylon monofilament.