Yes, I think Liverpool didn't perform too badly and they even managed to bring home a point. This season Klopp has rejuvenated his squad and it is an update that should be appreciated. While Chelsea have also appeared with a new face this season, Pochettino's arrival has certainly lifted the team's degree from last season's slump. I believe this season the Blues will again be able to compete in the Premier League even though it is quite difficult to dominate the top.
hopefully Chelsea and Liverpool can still compete with other teams which I think they are no less strong than the two of them. Man City, United and Arsenal are the strong favorites this season. Chelsea and Liverpool must be able to make their performances more stable and try not to drop points if they want to compete. I'm not saying they're weak, but these two might struggle a bit to compete for trophies this season.
Both Chelsea and Liverpool played good football in the first match of the season. But what happens is that Chelsea and Liverpool knows how to play draw in every of their meeting. So both of them playing together would not be the right criteria to determine whether the teams have improved. I can attest that Liverpool has improved right from the ending time of last season.
But there is no evidence of improvement in Chelsea apart from the pre-season. So we will need to see Liverpool play another club and Chelsea play another club for we to know if they have really improved.