performance - Is running a Windows .EXE inherently slower via Cygwin than via BAT?

Not the actual program, no.

Housekeeping and stuff before running the program may vary. Cmd probably calls CreateProcess directly. Cygwin's bash may first do argument parsing, wildcard expansion, fork via Cygwin's slow implementation and call exec with the parsed arguments, which Cygwin has to piece together into a string again to pass to CreateProcess. But in the end, a new process is created which has no ties to its parent anymore. So how fast your program runs entirely depends on that program, not on who launched it.