In what aspect ratio shoud one record with a DSLR?
When you take a photo with a Modern camera "usually" it's 4/3, I know you can change the aspect ratio, but that's not my point. I assume, that the sensors of DSLR cameras are the same ratio, because they are created for the purpose of creating photos, aren't they?


Actually, no. Only low-end digital cameras (mostly point-and-shoot) use a 4/3 aspect ratio, because they were designed to match the aspect ratio of computer displays (which used to be 4/3). DSLRs use the traditional 3/2 aspect ratio of 35mm film. So if you set your DSLR to 4/3 (for photos), a part of the sides gets cropped.


  Wouldn't it be smarter, to record with the fullsensor, to get "more" of the image"?


Most DSLRs don't use their 'full' resolution for video because of technical limitations (mostly memory buffer, but also memory card transfer speed). For example: My Canon EOS 80D has a maximum resolution of 6000x4000 pixels for photos. However, the highest video resolution it can record in is 1920x1080p @ 50fps (IPB). IPB means every frame is recorded as a full frame, no interframe compression is applied. Recording 25 or even 50 frames per second at a resolution of 6000x4000 pixels would result in an absurdly high data rate that DLSRs simply aren't built to process and transfer. 


  What aspect ratio, should you put your cammera into, to get the highest resolution. 


Depends on your camera. Either the camera menu or manual will specify the available resolutions for each aspect ratio, possibly it's a seperate setting as well. This way you can tell what combination gives you the highest resolution. If you can't find the resolution specified in the menu or the manual, take a test recording with every setting the camera has, copy the files to your computer and check each file's resolution with MediaInfo or a similar program.



Note that apart from the resolution, the bitrate will have a much higher impact on your video quality than some pixels more or less. Make sure to get a fast SD card with a lot of space so you can always record at the highest bitrate (and I-frames only if that's an option with your camera). Also, it's good practice to film in the resolution that you want your final video to be in for more reasons than video quality. So if you're creating a video that is intended to be viewed on normal video screens, film in 16/9 from the start.