I think Compass is pretty much THE best school there is in Qatar. But of course, this is just my opinion, therefore subjective. I find the other schools very "in the box" , where as Compass is a bit more innovative in teaching methods and general ambience. It really depends on what you want for your child...if you want "streamline" ASD is your best bet, as you said, great facilities etc. DESS, of course, traditional English style, and the same goes for Doha College.
The other schools, well, see for yourself. I would not send my child to any of those unless I had to. But again, this is just MY opinion. I am sure other people think differently.
And about the Compass Campus, the school is relatively new, and they do not have a purpose built campus, except for the Madinat Khalifa campus. But I find they make up for that with the great effort they make and for their students.