Blitzmax Windows vs Linux?

Will a Blitzmax executable compiled on windows work also under Linux, or must the same program be first compiled on a Linux system?

You have to compile on the platform you're targetting.

In my own experience, windows compiled BMax apps tend to work fine under wine, but the native executables tend to run a fair bit faster.

The executable must be compiled independently for each OS.
However, windows executables can be run in Linux under Wine.

...duh