Especially in the Champions League Arsenal lacks mentality and they lose in experience to Bayern Munich because it was proven that they had so much difficulty when facing the German giants. If the problem is in the front line then for the Premier League they will also experience the same thing but the front line they have is quite productive in scoring goals.
I think they are just used to the premier leaguestyle of playing... they tend to perform better in premier league maybe because they've studied almost each team pattern and style of playing by competing with them frequently...on the other hand they are not used to the Bundesliga style that's why champions league is a hard one because it brings together different league teams with different playing styles
It's not about style I think, it's about complexity. The EPL teams are more trained in strength, tactics and so on, because they play objectively in the most difficult league in the world and in many cases it is actually easier for them to play in the Champions League against teams that have lower tempos, because then the tempo of the game will be set by these same EPL teams