standard sword

There's really no such thing as the "standard sword." The khopesh (often called "sickle-sword") of the Near East and Egypt was a one-handed, single-edged, curved sword designed primarily for cutting. They were originally made in bronze and later iron, and the blade gradually grew longer; most surviving examples are 50-60 cm. So when you compare it to later styles of sword, you'd be comparing it to similar one-handed, single-edged, curved swords like the kopis, falcatta, or falchion.

How did the Kopesh develop differently from the standard sword?

The sickle-sword probably developed from the epsilon axe; Dan Howard gives a nice illustration of probable development in Bronze Age Military Equipment, and William Hamblin talks a bit about it in Warfare in the Ancient Near East to 1600 BC:

Thus the Akkadian sickle-axe diverged into two different forms in the Middle Bronze Age: the curved sickle-axe, and the classic sickle-sword. The curved sickle-axe continued the original curvature of the haft, but kept the wooden haft and metal blade of the original. It seems likely that the sickle-"sword" is actually a version of the axe, where the original wooden haft and metal blade are combined together and cast in a single piece. This would have served to decrease breakage both of the haft and the joint between haft and blade. [...] During the Middle Bronze Age the new sickle-sword spread rapidly throughout the Near East, appearing in Elam, Syria, Canaan, and eventually Egypt. Egypt seems to have been the last region to acquire the weapon.

Spalinger in War in Ancient Egypt: The New Kingdom adds:

The virtual monopoly of the Nile waterway, a perfect conduit for trade and political control, effected a stasis in Egypt with respect to the art of war. Those lands that frequently fought, on the other hand, were not blessed with such a peaceful condition. Hence, the tug of war between defense (armor) and attack (axes, swords) did not take place in the Nile Valley. When, however, the Hyksos took over the north during the wakened period of Dynasty XIII, the situation altered.

The move to sickle swords in Western Asia provides a good example of this dichotomy. The blades were relatively short, and in many ways this implement can be considered to be similar in purpose to an axe. Later, the blades were extended, a result of the growing use of defensive armor. At the same time the Egyptian axes were converted to piercing types [...] indicate how the Egyptians had to adapt their weapons to new developments.

I've seen some speculation that the "hook" at the tips of some khopeshes were used for grabbing an opponent's leg or pulling their shield out of alignment; Harman gives an example of that:

The inside curve of the weapon forms a hook that can be used to trap an opponent's arm, or to pull his shield out of the way.

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Did the ancient Egyptians have the style of sword we generally attribute to medieval England?

Medieval England would have seen a lot of swords in Oakeshott's Typology, which were generally: iron or steel, straight, double-edged, single-handed blades with a crossguard, although there were many variations in size, shape of blade, etc. Ancient Egypt never had an exact equivalent, but they did have straight-bladed, double-edged short swords (mesu and neken) which were similar to (and probably based on) those of other Near East and Mediterranean civilizations. There's a bit on that by u/Karvina in Did the unique design of the Egyptian khopesh have anything to do with the limits of the metals of the era?

What are the pros and cons of a Kopesh (both in general and compared to a medieval sword)?

Curved swords, especially those with a forward curve like the kopis or khopesh, are good at chopping, combining something of the piercing ability of the axe while retaining the ability to do draw and push cuts (where the blade is drawn or pushed against the enemy). The curve, however, makes them less effective at delivering a thrust (especially with bronze or soft iron, where the metal would have a tendency to bend or flex where you want it to remain rigid) than straight-bladed weapons of the same size. Probably the largest problem with the khopesh design was the material: while bronze can make for an effective (and deadly) slashing weapon, it is not as hard as steel and hitting it against something hard (like bronze armor, bone, or iron weapons) would probably notch and ruin the edge in not too many blows. Other than that...well, there were single-edged, one-handed curved swords designed for slashing in medieval Europe, like the falchion. So the design itself isn't necessarily bad.

As compared to a "medieval sword", the ancient Egyptian khopesh would have suffered a couple disadvantages in any kind of one-on-one fight (assuming all else being equal). One: material - the European blades of the Middle Ages were made of iron or steel. Two: reach - European one-handed swords were often longer, and so users would have more reach for thrust, parrying, etc. Three: the guard - the cross-guard, while not the most developed of guards, was still more substantial hand protection than the khopesh itself gave.