System Information
win7 64 k2200

Blender Version
Broken: 2.78

Short description of error
fbx and obj/collada/etc have a different concept of the "apply modifier" option in the exporter panel.
obj apply what you see in viewport, very intuitive.
fbx only what you see eventually in render. So there is not a visual feedback .
collada let you choose. (very good)

Exact steps for others to reproduce the error
compare the obj with the fbx files to understand what I'm talking about.

ps: I know that unchecking the "render" icon from the modifier stack prevent the modifier to be exported, however I think the term "apply modifiers" should be consistent among the exporters.

thankyou