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.
The season has only begun, thus we shouldn't begin to emphasize either team's improvement until Chelsea and Liverpool have played their other matches, as you correctly point out. By that time, we can assess whether or not both players have improved since the season's beginning.
For Chelsea or Liverpool, winning another is difficult. Their match frequently ends in draws. Having them play 15 draws so far. If I were to place a bet on their return leg at Liverpool home, I would immediately do so as a draw match.