I found several explanations how to convert an image to outline image but I would like to have also the details from the image like below.
Could someone give me some clues how I could start to do it? Is it better to use Photoshop or Illustrator?
You have actually already got a working answer - drawing is a way to make drawings and Illustrator is quite good program for drawing. It's not especially difficult if you keep a photo under your drawing as a reference (Only remember to lock it to keep it in place) We call it "manual tracing".
Today electronics designers generally can easily have 3D models of their creations. Component makers give the models of the components and the circuit board design program can create the rest. Alternatively one can place the parts onto the circuit board model in 3D CAD program. Unfortunately a 3D CAD program which allows making assemblies easily is costly. That property is often disabled in low cost or free versions. Easy = put this part to these holes, rotate and move it automatically to fit exactly.
The illustration like drawing is a projection of the model with selected details. It's a vector drawing, not like a photo. It can generally be imported to Illustrator for artistical retouch and explanations.
Here's a 3D model of RaspberryPI ver.B board seen as wireframe, hidden lines removed, no edit is attempted because I can only view this type of 3D models.
Just for curiosity I tried to save the 3D scene as PDF, open it in Inkscape and color one surface & add a random text:
All this is also possible in a 3D program which is sophisticated enough to edit models. Unfortunately the available models usually are structureless geometry only versions, typically STEP-models which need something more than cheap- or freeware to be edited. I haven't it. But the sellers often also provide PDFs from where one can extract line art drawings.
About your photo:
You can make a sharper greyshade photo with exaggerated edges easily in Photoshop, if that helps you:
At first duplicate the image layer. Transform one of the copies to a good black-white mix with Image > Adjust > Black & White. Then with Filters > Others > High-pass cut out from the other copy all but the edges. Insert contrast to the filtered version with Image > adjust > Curves or levels. Keep the mid brightness at 50%. Blend the filtered version with the BW version with layer blending mode Hard light. Reduce the opacity, if needed.
In the left you see the filtered version with increased contrast and in the right is the blended result.
Of course, it's only apparently sharper. The second glance + zooming in reveals that it's still the same low resolution and noisy JPG. If you can decide the resolution, have it at least 2000 pixels wide. Then it can be sharp enough with no tricks, but it can be better with sharpening. Here's nearly the same board as your's sharpened like your board above. The used photo is a much higher quality version:
Illustrator. There is no automatic 'conversion' for this, you need to redraw each and every line by hand or have somebody else do it for you. See this video for a basic idea of what needs to be done: https://www.youtube.com/watch?v=ZV8PT2Xh04I