Those example do not show that Hercules is more powerful then Ares but that he is the better fighter. A power person can lost to in a fight to some one less powerful. Captain America is less powerful then most lower tier Bricks such as D-man; however, Cap will beat D-man more often than not.
Again, I stand by what I say that Ares is more powerful then Hercules. I do agree that Mortal Hercules is at least as physically strong as Ares and I accept your example of hims winning but he is still not as powerful as Ares. Those example shows that Ares is often depicted as a wuss despite his power. I am not saying that the mingling of mortal and god can produce someone with more power then a pure god. However, I most case that is not so and Hercules is not more powerful than Ares. He is the better fighter and the greater hero but does not have more power. Let put it this way. If Ares was a "champions character" he would cost way more point to make then mortal hercules.
If we are talking about variety of power than I can agree that as a mortal Hercules is not as powerful as Ares. In powers related to fighting Hercules is superior or equal to Ares, but lacks the mystical powers and immortality.
However, as a god I think it is clear Hercules is superior to Ares. Herc has the same healing factor if not better along with greater strength and durability. Since godhood is often treated as just getting rid of the mortal half of Herc which seems to weaken the godly half by denying it the immortality aspect once Herc has that part removed and his pure god have is unimpeded it is clearly more powerful than Ares. Whether or not Hercules has other mystical powers or can develop them is another matter. Gods are often stated to all have the capacity for some mystical power, but few ever bother to develop it. Hercules's distrust of magic and focus on the physical would lump him into the group of those that do not.