Now, this is not entirely easy, since I never did a careful analysis of the differences. However, I started playing the dark eye in 4.0 and later switched to 4.1, I GM quite a lot and know pretty much all the books by heart by now, and this is what I noticed:
Production Quality. Not what you asked, but from 4.0 to 4.1 The Dark Eye went from a ridiculous number of different softcover magazines to a few big, bound books, sorted by topic - you can get the basic rules in one, ALL about magic in 1 + Liber Cantiones, ALL about the gods and demons in one, ALL about alchemy in the next and so on. Also, the overall layout and descriptions have gotten a lot better, and some smaller contradictions were taken out that resulted from having multiple books on everything.
Balancing. Some things that were truly broken got changed - an example for this is the ability for guild mages to store spells in their staves. This used to be one of the most broken things a mage could do imo, now getting them out actually requires you to manage a check that gets harder both with how many spells you stored and how complex they are, making it much less a jack of all trades for any mage. However, that means you can now use any spell stored instead of just the last one. Mind, however, that there are not that many big changes in balance - most of the things remained unchanged, only what was truly broken or unfitting got amended. All Errata until 4.1 also got implemented.
Lore. A lot of lore has become a lot more consistent; however, this just goes back to the production quality since it was mostly different books stating different things before.
I also feel that there are just a lot more books on topics such as regions and different cultures now.
All in all, there are no truly big changes to the rules - officially, DSA 4.1 is the rules of DSA 4.0 plus the Errata, summarized in well-organized books with a high production quality. Its no absolute necessity if you are currently playing with 4.0 and happy with it, since the rules dont change that much.
However, I consider it significantly easier and nicer to read the new books, they fit together very well and make it significantly easier to get into the game if you did not already due to the separation of the books. I can highly recommend them if you want to start with DSA 4.1 - however, if you already have DSA 4.0, you can slowly start changing out the boxes to the 4.1 books and wont notice any large conflicts apart from the new books just being SO MUCH NICER to read than the old ones.
EDIT: Thanks to malexmave for linking me this. However, the 7G - Campaign (Borbarad) does not mark the transition between 4.0 and 4.1, and thus has nothing to do with this question. 7G has happened in the 4.0-Rules already.