There's a lot of literature that point towards more application-specific optimization in the lowest levels of the operating system, for example the Exokernel papers are an early example of this. More recently, you may want to have a look at the the MirageOS paper(s).

Here's my bit of uninformed speculation: presumably a lot more potential for aggressive optimizations. It's unlikely that you can make Linux as bare-bones as you could a unikernel. Besides, for all intents and purposes, you can't run Linux through a whole-program optimizer along with your application (not sure if this is even a worthwhile objective). I would also think that communicating between the application and the "kernel" via function calls instead of system calls would yield some non-negligible performance gains as well.

There may be some, but even if there isn't, some benefit could be the ease in which you strip it down.