Thanks guys for your help!
The composition settings were the same in both applications,
when talking about the preview monitor I meant the left one in
Premiere.
I tried a lot of things but the results were still the same:(
The only solution that showed some improvement was when I exported
the finished project from Premiere to a quicktime file, animation
preset, and millions of colors +. But only when I would not
deinterlace it. Still, not deinterlacing made it look slightly better
but then you could see the lines and some artifacts were added:(
Any ideas?
Thank you again!
AVL