I grew up and Hamilton and haves lot of Accies supporting mates. Apart from last season, we always finished in a higher league position (or higher league!) than them. The derby matches were always their way of getting bragging rights regardless of the final league stats.
The slaggings would last for weeks afterwards, so always happy to beat them any way we can. In the grand scheme of things, however, we have never really been significant rivals, which is why I think our players and fans have more emotions invested in beating a team like Hearts.