Using dis to look at the bytecode generated for the two versions:

not ==

4 0 LOAD_FAST 0 (foo) 3 LOAD_FAST 1 (bar) 6 COMPARE_OP 2 (==) 9 UNARY_NOT 10 RETURN_VALUE

!=

4 0 LOAD_FAST 0 (foo) 3 LOAD_FAST 1 (bar) 6 COMPARE_OP 3 (!=) 9 RETURN_VALUE

The latter has fewer operations, and is therefore likely to be slightly more efficient.

It was pointed out in the commments (thanks, @Quincunx) that where you have if foo != bar vs. if not foo == bar the number of operations is exactly the same, it's just that the COMPARE_OP changes and POP_JUMP_IF_TRUE switches to POP_JUMP_IF_FALSE :

not == :

2 0 LOAD_FAST 0 (foo) 3 LOAD_FAST 1 (bar) 6 COMPARE_OP 2 (==) 9 POP_JUMP_IF_TRUE 16

!=

2 0 LOAD_FAST 0 (foo) 3 LOAD_FAST 1 (bar) 6 COMPARE_OP 3 (!=) 9 POP_JUMP_IF_FALSE 16

In this case, unless there was a difference in the amount of work required for each comparison, it's unlikely you'd see any performance difference at all.

However, note that the two versions won't always be logically identical, as it will depend on the implementations of __eq__ and __ne__ for the objects in question. Per the data model documentation:

There are no implied relationships among the comparison operators. The truth of x==y does not imply that x!=y is false.

For example:

>>> class Dummy(object): def __eq__(self, other): return True def __ne__(self, other): return True >>> not Dummy() == Dummy() False >>> Dummy() != Dummy() True