Update
The BDFL (Benevolent Dictator For Life) has spoken, and the Enum documentation
has changed to reflect all upper-case member names.
The examples in the [previous] docs are lower-case primarily because one of the preexisting modules that Enum was based on used lower-case (or at least its author did ;).
My usage of enum has usually been something along the lines of:
class SomeEnum(Enum):
... = 1
... = 2
... = 3
globals().update(SomeEnum.__members__)
which effectively puts all the members in the module namespace.
So I would say whichever style feels more comfortable to you -- but pick a style and be consistent.