Kylo beats squidly-diddly.
He was able to fight effectively even with a serious wound in his side. He defeated Finn (although Finn acquitted himself well) and held the upper hand against Rey until she fully let the Force in (that bit when she closed her eyes and centred herself). Imagine how he'd fare at full health.
Also Kit's style is lousy at 1-on-1 duelling. True, he managed to block a few strikes from Palpatine but that's partly due to Palpatine's sloppiness.
Kylo will be dining on fried calamari that night.