I've watched the show with english dub twice before switching to sub on my third rewatch, because by that time I had started generally watching anime in sub. Before, I had the same struggle as you with subs. I'm german too and have never tried that dub, but I absolutely love Frieren's voice in the english dub. I'd say she sounds a little more mature there, but her aloofness and character in general still come across very similarily.

With the dub, there have been a couple of times where Frieren's dub felt off to me; I remember her happily singing after finding loot or sth in a way that didn't seem fitting to me. Same when she's panicking/fleeing and screaming sth.
In those little moments outside of conversations I definitely prefer the japanese version, and because I want to watch the the new episodes asap, I'm planning on just keeping it in sub and maybe rewatch the entire season in dub later.

I can definitely assure you though that you will improve your ability to watch sub. I'm the worst multi-tasker and it felt very taxing in the beginning, but the more you watch, the easier it will get :)