Actually you are somewhat correct, but incorrect.
SC2 is widely regarded as the best SoulCalibur game, in the evo competitive scene, and among casuals.
SC1 is regarded as the best SC game overall, and is the only SC game, to get a perfect score of 10 out of 10.
The gameplay in SC1 is also way more advanced than SC2, and has lots of quality of life stuff, that were literally and deliberately removed in SC2.
One of the head Japanese dev guys who worked on SC2, many years ago, actually admitted that SC1 is a more advanced, fuller game than SC2. SC2 was deliberately watered down according to him, to appeal to both casuals and Tekken players, who did not understand sidestepping and full 3d combat. And they deliberately threw in guest characters, to easily get people to buy it, and make a quick buck. The whole SC2 thing, according to him, was all business as he put it.
Well in the US and certain countries there is always lag. No surprise there. Strangely enough for certain dreamcast games, there was seldom lag in Japan. In the case of PS2, it does not surprise me that lag was a thing.