The first expression should read (x != 1).  You have an extra = in the first one.  The second one does require 2 =, as you correctly wrote.

In this case, they will give the same result.  The first one is slightly preferable since it can be done in a single operation. 

In the first one, you are asking "is x not equal to 1?"  It is a single question.

Vs the second express, which says "is x = 1? ok, now give me the opposite of that."