Steel weapons are going to outperform bronze weapons, full stop. They're lighter, hold edges better, and can take more abuse. It is simply a superior material from which to make weapons. Trying to compare Weapon A made from steel and Weapon B made from bronze and saying the results prove the design of A is inherently superior is disingenuous at best.
Probably the bigger reason why most swords are straight-ish is that they are easier to produce. They also work better for stabbing, which is handy when you're trying to punch through or around armor. The khopesh is a hacking weapon, which means it would be far less effective against something like, say, a Roman centurion's cuirass.
It's worth noting, however, that throughout history axes in general have been very effective weapons, existing alongside swords up to the widespread adoption of firearms. So I wouldn't say that a khopesh made out of modern materials would be ineffective. Hell, made out of bronze it sure seemed to kill people just fine if its widespread use by the Egyptian empire is any indication.