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
I don't understand that you said Arsenal used EPL style in playing, is there is a specific style of playing in EPL? I think there is no difference with other league, every team used almost the same style.