I like Gamestudio3D (flexibel / no nonsense, helpfull community) but they need to fix that damn ATI incompatibility with heavy games (or atleast with my heavy games :p).

Unity xbox360 / xbox one / win8 / windows phone for free if you are a unity pro user:
http://blogs.unity3d.com/2013/06/27/build-conference/

I took a look at the newest Unity version yesterday again. The editor is still an eyecatcher and the rendering including shadows etc looks nice. But the learning material is a mess! There are 1000 tutorials for beginners but no structured one for people who are experienced in game design. Furthermore, I only found video tutorials and no written one that explains building a simple 3rd person game.

there are written ones too, and some example projects, I downloaded them probebly from unity webpage a while ago, but for Unity 3. video tutorials are very time consuming, I use them very rarely... I found a link now : http://unity3d.com/gallery/demos/demo-projects

Well they have more or less lately started their "Learn" segment so there currently just are rather basic things plus the Stealth project which I think is pretty great for a free tutorial. More advanced stuff is going to take its time as tutorials (especially good ones) don't write themselves...

Apart from that one can find extensive amounts of tutorials in the teaching category in the forums - I especially liked what BurgZergArcade did: http://www.burgzergarcade.com/hack-slash-rpg-unity3d-game-engine-tutorial

Looking for written tutorials probably limits the amount suitable tutorials as video tutorials seem to be what most people ask for nowadays and I see why this is (it has its cons when you want to go back to a certain step but good video tutorials are way more easy to follow since there can be extensive comments on the code written and for explaining things like the editor videos are superior to a written text)...

Written tutorials over video tutorials anytime, dont want listen hours to some nerdy voice (my rule of thumb; only do 'voice casting' when it is above average). Plus you have to press pause all the time etc. *continues reading the gamestudio 3d manual*

hehh, unity 4.2 free now features hard shadows for sun, and some level of navmesh pathfinding (I found no exact definition of it). do they want to kick out 3dgs free?

Yes, maybe, but I think they won't succeed. 3DGS is very easy to use, but Unity isn't. I've tried to use Unity, but I dropped it away, because it's too hard to use.

Serious question: Can Unity do everything 3DGS can do? I mean, with 3DGS you can in theory realize any game you want to make - be it a multiplayer shooter or some Skyrim style RPG or the next Diablo or even a World of Warcraft clone.
Unity seems to be less flexible on first looks, didn't work my way into it yet though. Should I switch to Unity while I still can?

I have only little experience with unity3d, I prefer 3dgs, especially after I upgraded to commercial, a new world opened up.
unity is definitely a well developed engine having a lot of advanced features (mainly available only in Pro which is very expensive), and more up-to-date in technology, has a nice editor, but requires some 3d knowledge to start with, and a bit more organized work and pre-designed game concept because of object oriented programming. its editor has a lot of features what makes life easier, and what I would like to see in the new WED, like terrain editor, vegetation editor, particle editor, and how game objects can be built up from components, and everything can be seen in real-time.
personally I like the simplicity of 3dgs usage in contrary with unity omplexity, but in 3dgs there are a lot of things you have to do by yourself if you really want to utilize all the engine features effectively - this is why I made my own game editor instead of using WED.