Exactly this is crucial test for both teams. Win would be huge boost and prove they are serious title contenders. You argue that Liverpool as defending champions have advantage because of their experience and consistent form. Your idea that since Arsenal beat Manchester United and you think Newcastle is better than Manchester United then Liverpool should be even better than Arsenal is creative way to look at it. This match is chance for Liverpool to show their dominance and for Arsenal to prove they can challenge best.
Even this thinking is correct, that in fact is not accurate and logical, in football, a winner and lose in a direct match only can be known after a referee makes his final whistle. Both Liverpool and Arsenal are very strong and ambition so they are able to score a winning goal anytime or can make a comeback within only several minutes. Therefore, assessing which team are strong and will be the winner before the match is very non sense.
This is a big match for both teams in the Premier League, and both are eager to prove their best after marking the start of the season. A win will certainly be a motivator for either team, as it will be the beginning of a title challenge. The reasons could vary depending on which team will win the match, but I see it differently, as there is a possibility of a draw, reminding both teams that they will be cautious enough to avoid dropping points. The goal productivity of both teams is also balanced, only Liverpool is slightly better because it managed to score seven goals in the previous two matches, so that does not mean Arsenal should be underestimated because they also managed to score six goals in the previous two matches.
Liverpool are the champion and they are defending their title while Arsenal definitely want to win a first big title with Arteta after they already finished three latest seasons in Premier League at a second position. Liverpool are more attacking in playing style but it's dangerous when playing against Arsenal that have changed a lot in latest seasons with Arteta management.
Arsenal with Arteta management have changed and they are no longer obsessive with ball possession, passes and beauty football llike with Arsene Wenger and other previous coaches. Now they are focusing mostly on results and aim at winning their matches even they have to sacrifice ball possesion, play boring and only wait for penalties, corner kicks or free kicks to score a winning goal.