When is a Scimitar better than a Longsword?

The longsword deals 1d8 slashing or piercing damage. The scimitar deals 1d6 slashing damage with the forceful and sweep traits. At first glance, it seems that the scimitar might break even for damage with the longsword only when there’s a reasonable chance of hitting a third or more attack in a turn. Considering the rarity of that, the scimitar comes across simply inferior to the longsword (in terms of average damage per round).

The scimitar is a thematically cool weapon, though, and I’d like to see it be useful.

In what circumstances does a scimitar outdamage a longsword?