Originally posted by Eric Lemaitre:
you can switch company with H1.
You can switch companies on an L1, but you would need to qualify for another working visa which may or may not be available to you at that time.
while with L1 if you loose your job then you automatically loose your visa and must bail out of US (except if an AOS is pending).
When you lose your H1 job, you automatically fall out of status as well.
Cheers!
Luke