Ok, for the case of Crit Mod +1 and Crit Range x2, the following is a chart of average damage per swing as a function of bonus base damage.
(Bonus base damage can come from stat modifier, deadly, enhancement bonus, power attack, etc):



By the time the bonus has reached 3 (yes only 3), the khopesh is on top and remains so, forever. The slope of the khopesh and scimitar lines is 1.55, whereas the longsword and BS have a slope of 1.35.

If you consider a Seeker +12 item, the slopes are the same, but the divergence is immediate from the start. The khopesh is always #1, followed by the scimitar:


So I think that settles it: khopesh is better than scimitar, but the difference becomes increasingly less important with higher base damage bonus. With a base damage bonus of 20 (not hard to reach!), the difference is 4% (without a seeker item).