Sorry about not chiming in earlier. Since I am not familiar with the Amsoil product I'm not in a position to do a comparison. However, I can address a few issues about Fluid Film here:
Fluid Film has no solvent content and will not dry. It is the non-drying characteristic that makes it last so long. You could realistically get a minimum of twelve months of coverage from one application in areas that are protected from UV rays; such as hinges, locks, and garage door runners, where the product is not subject to constant abrasion. In a completely enclosed environment, Fluid Film could provide a permanent solution.
Fluid Film will certainly help under mower decks if proper steps are taken. The deck needs to be clean, and a few good applications are necessary to allow the product to saturate into the pores of the metal, where it sets up a barrier of slick protection.
Fluid Film is very cost effective if you understand its performance. Like I said, I am not familiar with the Amsoil product, but Fluid Film has outperformed every product we have tested against.
Because of Fluid Film's unique properties, it is available for a multitude of applications unavailable to similar products. It is safe to use on paint, plastic and synthetic rubbers, and will not burn greenery or freeze. It is an excellent snow release agent and will keep locks from freezing, snow blower chutes from clogging and electrical connections from corroding.
If you spray Fluid Film on an old, oxidized paint job, it will bring the luster of the paint right back.
I'm not knocking the Amsoil product at all. I'm just not familiar with it.