https://www.youtube.com/watch?v=AQDr13TyLJ8
Even if heavy cloth protect you from saber cuts, saber was preferred over straight sword when metallic armour fell out of fashion. Can we say that saber is more efficient than straigth sword against heavy cloth ? There must be a limit to the point where heavy fabric armour like jack/gambeson is completely proof against saber cut ?

The last official cavalry sword patterns for the British Army were the 1908 and 1912 (Officer's) swords. These were both straight, thrust only swords. So for the British Army at least the debate between thrust and cut was won by thrusting swords.
For the rest of us the debate still continues :D

Mind that in World War I many cavalry troopers (especially in the Middle East) sharpened their 1908s to make highly serviceable cut-and-thrust swords.