Which notebook should I buy? (17", 700-800 euro)

They are all 17.3in, i7 and gt840m. The Aspire Nitro is the only 1080p. The Asus is the best quality and has more ram than the Nitro. So I'd go with the Asus.

Alex, you say portability is not an issue. Does that mean it is going to sit on a desk all the time and once in a while used 'on location' like a kitchen counter or workbench in the garage? Does that mean it doesn't need much battery life, as it will always be plugged in?

The U series processors (e.g., i7-5500U) are long on battery life, but short on performance, from what I can see. When considering a laptop, head over to cpubenchmark.net and take a look at the performance specs of the cpu. There is no reason to pay for an i7 that doesn't perform as well as an i5, unless battery life is an issue. As an example, that 5500u is considerably slower (in benchmarks) than a second gen i7-2630QM. The trade off is TDP and features (off the top of my head, the 4th & 5th gen i7 support 3 monitors, but the 2nd gen only supports 2, iirc).

Also, what is your price range? The Dell sells for ~$500. At that price range, I would take a look at a refurb Dell XPS or Precision on eBay. There are some excellent deals to be had.

Finally, video card. Unless you are planning on gaming, you probably don't need a dedicated video card. The newer i5 & i7 processors all support multi-monitor -- that is, they have a GPU incorporated in the CPU. If you are serious about CAD or video editing, then you need more of a workstation video card. The Dell Precision laptops ship with either a AMD FirePro or Nvidia Quadro. If you are not serious, I would research to see if there is any real world CAD or video editing advantage to a dedicated card such as the 840m over the integrated GPU Intel has.

BTW, of the laptops I have purchased over the past few years (10+?), I have been consistently disappointed with those that I purchased based on specs. I now rely much more on reviews. Professional reviews are fine, but I read a lot of user reviews. If everyone is complaining about a specific item, such as the touch pad, I probably will have the same complaints. I've learned that the hard way.