I want to build a passively cooled system, I can't really decide what CPU would be most suitable for such system. On one hand Intel have from what I can understand from various benchmarks I have read a lower power consumption and fast CPU while AMD got a much faster GPU.

However being the system is going to be passively cooled, I am in need for some advice on which CPU to choose and if AMD runs cooler than Intel.

What's the main use for the system, which OS will you use?
What kind of cooling do you want, big passive heatsink, heatpipe case, ... ?

I will use the system for programming, media production and a home-server when I am on the road, now and then I would appreciate a few games of Quake Wars.

The system will be operated by GNU/Linux. I am going to use a mini-itx motherboard and most probably though not set in stone a thermaltake HR-02 alike:

If you don't need 3D capability or some odd feature Intel has crippled out of its low-power offerings, the obvious answer is Intel.

You should read some of Phoronix' processor benchmarks, specifically on the Intel Core i7 3770K and AMD FX-8150 Bulldozer. You should look what benchmarks are relevant to you, the performance using Linux can differ a lot from the Windows performance.
These two processors (with the i5-3570k) are probably the shortlist. Their idle power draw is very similar, but Intel processors draw less power when loaded and are easier to cool.
I'm not sure if you can cool any of these completely passive, even a very slow spinning fan (<500rpm) will improve the cooling dramatically and is inaudible. I would highly recommend it, especially if you load the CPU with compile jobs for long periods at a time.