Which is better for a Motto: Come as a Stranger, leave as a friend. Come a stranger, leave a friend. Why?

Second way is better.  

Saying "as a" implies "kinda like" or "sorta"  (but not really). 

The second way is definitive.  

The second is better for a few reasons. First, it is more memorable because it is shorter, the contrast between stranger and friend is more clear, and it is more difficult to forget or distort. Second, it evokes an imagine of someone arriving as an unknown, but leaving as a friend.

Come as a stranger, go as a friend.

Arrive a stranger, leave  a friend.

This is a common motto - used by the Mister B&B gay-friendly travel site - among others.

The opposite of leave is arrive.

This motto already exists in its correct form. ("Arrive a stranger, leave a friend.")