The scimitar breaks even with the longsword on your third attack if it hits, and may gain benefits if you are attacking multiple targets instead of one. It can surpass the longsword (very slightly) while the wielder has 4 attacks (such as being quickened or with a class feat that provides extra Strikes for the same Actions).
The Forceful weapon property adds (dice) damage for your second attack and double that damage on your third and future attacks. The result is that your first attack is made at less average DPR than the longsword, the second equal, and the third higher (by the same amount that the first was reduced) equaling net neutral unless you Strike more than 3 times.
The Sweep weapon property helps with this if you're willing to spread your attack against enemies surrounding you. You gain +1 (circumstance) bonus to hit any creature you haven't attacked yet.
The bottom line is that the scimitar is strictly weaker than the longsword for most characters. Even used in its ideal circumstance, it equals the longsword in DPR but has lower maximum damage and only shines when wielded when surrounded or in similar circumstances. There are builds that could benefit from its use, such as a Flurry Ranger with Two-Weapon Warrior archetype, but it would have to be something equally specific or with specific benefits to the scimitar, such as Sarenrite Warpriest Cleric.
Another edge case is that you may be proficient with scimitars but not longswords, although current options for this seem rare. As of writing, I only see Catfolk Weapon Familiarity and Pirate Weapon Training.