I am no expert, but Rapiers are for precision thrusting witht he point delivering the lethal point of attack. A Khopech is a chopping/slashing weapon where the blade edge is the lethal point of attack.

Naturally, how you use a slashing weapon is very different from a piercing weapon.

Here are some assumptiosn from a layman's point of view (i.e. worthless):
1. I am going to assume that a rapier has the range of attack advantage over the Khopesh so they would probably want to stand-off a bit more, while the Khopesh user would want to get in close to deliver the killing blow
2. The Rapier user would want to keep the traget in front, while the Khopesh user would not need to do this
3. Swings with a Khopesh are probably less well controlled than a lunge with a Rapier.
4. Like most blade fights, position, distance, and foot work are the key to victory