It is likely that Manchester City and Arsenal regularly do well in the Premier League as Manchester City and Arsenal do not have tough opponents in the English Premier League but this is the same thing we do not see in the Champions League. Manchester City is doing well in the Champions League but Arsenal is not doing very well in the Champions League. Arsenal's Champions League journey has come to an end after going from group stage matches to the last round of the Super Sixteen. As the big teams are competing in Champions League, Arsenal and other teams should compete hard so that Arsenal and other teams can finish the tournament in a better Champions League stage.
Arsenal and Manchester City have shown their ability in the Premier League by defending as champions 1 and 2 in the last 2 seasons so I think it's true as you said that they are still very strong in the Premier League their opponents are still below them but don't forget Liverpool because this club will also be a strong competitor in the Premier League last season this club became champion 3 this season maybe there is no significant difference Arsenal and Manchester City will definitely be at the top of the EPL standings.
Talking about the Champions League Man City and Arsenal are different Arsenal does not have a good experience it always ends before the final last season Arsenal was eliminated by Bayern Munich in the quarter finals.