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 first games are always tricky and it is difficult to know how stable the teams are. With new players requiring time to adapt to the team and to the strategy used, things gonna improve later.
Liverpool will face Bournemouth in the next round so a victory should occur or else it will be a bad start for them. Chelsea will face West Ham which isn't that easy so they will have to show their best to win.
Tottenham Hotspur - Manchester United and Manchester City - Newcastle are the best matches this weekend.
As you just mentioned it is difficult to know where the teams are heading so early in the season and that is why I think that the most interesting game of the upcoming weekend is Manchester City vs Newcastle United. Obviously, Manchester City had a comfortable win as expected, but many eyes were watching Newcastle and they won destroyed Aston Villa, which could be a first sign that Newcastle will once again be in it for the top 3 or top 4 of the table. Now how are they going to play in an away game against Manchester City? It is impossible for me to come up with an educated guess, I have no idea whether the 5-1 can be considered as a good reason to think that they will do well against Manchester City, too. It doesn't have to be a win against them, but a draw or a very close match that does not end 3-0 for Manchester City would still be a respectable result.