So which direction do electrons really flow?
Conventional current goes from positive to negative, which is the opposite of electron flow which goes from negative to positive.

Neither the electrons nor the holes are responsible for doing the work, it's simply the flow of charge that does the work. The direction of the flow of charge, the electrons, or the conventional current, is not relevant to the amount of work that is being done.

In electronics, when we say "current", we refer to conventional current. If for any reason would we would want to refer to electron flow, we make sure to say so.

The reasons for this are mostly historical.