Well, I think there might be more similarities, but of course, if I'm wrong, feel free to correct me....
Both Amiga and Unix can be controlled entirely from the command prompt, and that the command prompt is always there, even if you can't see it...
the ' . ' and '..' commands to go up one level, and to the root directory respectively... although in AmigaDos it's '/' and ':'
Both have more types of file protection bits than windows (I believe)
And there is more, I'm sure .... hmm, the ixemul.library ...
The Amiga 3000UX won 'Best in Show' at the UnixWorld show, does that count?
Well, IIRC all (or at least most) of the DOS commands are the same in that sense, that e.g. in AmigaDOS you say "copy", while in Unix you use the abbrevation "cp" (that you could also use in e.g. Commodore Basic v4.0 instead of the full commands) - the syntax is the same.
I remember that back in 1989-1992 during my CAD studies - where I learned UNIX - I found it quite easy to learn the UNIX commands and their syntax because of the similarity to AmigaDOS.
As far as I remember Unix even had a directory structure similar to the Amigas directory structure back then - but since my CAD studies I had no root access on a UNIX machine to verify this...
Root Directory - that was one of the differences I remember and is related to the multiuser capability of UNIX that the Amiga does not have by standard (I know that a MultiUserFileSystem (MUFS) exists for PFS3, but haven't testet it so far).
I think only a person with admin rights had access to the root directory, as the system resides there.