Ok, let's analyze this empirically. If what you (and others) say is true, we ought to be able to show it explicitly. I have created the following comparison for base weapons, "other things being equal."
The bottom 4 rows are average damage per swing.
Keep in mind, I assume 1 is a miss so I do not include it in the calculations. Based on simple base damage, BS comes out on top. Based on changing crit range (Improved Critical Feat, etc), it's still on top. Based on crit modifiers, it's still on top. Based on both, it's still on top.....
Also, longsword still comes out ahead of rapier and scimitar every time.
To keep this focused, let's discuss:
scimitar vs (Longsword/Khopesh/BS)
Not khopesh vs BS vs Longsword.
How could a scimitar really compete, all things being equal? What crit-based enhancements/modifiers make it more worthwhile, in your opinion? I'll add them to the calculation and we'll see what's best!