The question is not well phrased. It's like asking "Which is a better tool: hammer or screwdriver?" (Answer: it depends...)
The better question is "which is a more effective martial arts technique?"
There is no historical basis to support the claim that slashing weapons were generally cavalry weapons.
Here are some relevant historical examples:
Swords were by far the preferred weapon for cavalry in the 1800's. Much preferred over revolvers even.
The British issued their cavalry a curved saber primarily designed
for slashing. This is because of the lessons they had learned in
India and Afghanistan where slashing weapons heavily predominate.
The French, however, issued straight cavalry sabers and were heavily
trained to use the point. The superior deadliness of the point to the
edge was known in Europe since Roman times. Traditional
dueling wisdom held that one wound from a sword point equalled three
injuries from the edge.
In French vs. British cavalry combat, it was discovered that very few French would emphasize thrusts instead of slashes (usually only French officers would rely on thrusting in combat). The French learned that in the heat of combat, slashing is the natural reaction of even very highly trained cavalrymen.
In Roman times, the gladius was relied upon for six centuries. It was primarily used for hacking down an enemy (often after knocking him over by slamming into him with the shield) The gladius was generally used for stabbing mainly for the coup d'gras.
Metallurgy had progressed far enough by the Sixteenth Century to allow swordsmiths to make sturdy , thin, light, fast thrusting swords. For dueling, a long, thin, sharp sword (although expensive) was a vastly superior weapon to any slashing weapon of the time (like a cutlass) Additionally, pikes (long spears for stabbing) were very successful battle weapons (even against poleaxes - i.e. hacking arms-although there was no clear dominance. Mainly it was less expensive to equip a body of troops with pikes, and easier to train them.
Then, of course, there is the obvious example of the Japanese katana. For two thousand years, the Japanese never saw a real need for thrusting weapons.
Modern military blade fighting strongly emphasizes thrusting techniques, probably because slashing techniques do not work as well against people wearing modern clothing and carrying kit belted and strapped to their body.
Nevertheless, Asian bladed martial arts place the emphasis on slashing -primarily out of centuries old traditions that rely on disarming an opponent FIRST (by slashing his hands and arms) then going for the kill.
Perhaps the most timely and relevant historical example is the example of the World War One trench raids. That was probably the last great era of hand to hand combat in close quarters, almost always at night, and almost always begun as a surprise attack. It was a time when an individuals' personal choice of weapon and technique was very likely to make the difference between life and death. Trench maces make good museum pieces, and they were used alot, but their prevalence in war museums doesn't mean they prevailed in the trench raids. British and French trench raiders tended to rely on thrusting weapons such as poignards, bayonets (often attached to a broomstick to make a pike), the "French Nail" (a bent tent peg) and Bowie knives. The British Gurkas however, gained fame using kukri (hacking) swords.