How compatible is the old xbox 360 with the xbox 360 slim?

Can you hook up the slim controller with the old xbox 360 and vice versa?

Can you do a system link between the xbox 360 and the xbox 360 slim?

If you can think of more compatibility questions to answer and can give me the answer, that would be great!How compatible is the old xbox 360 with the xbox 360 slim?
The consoles are exactly the same as far as what they support except you can't use memory cards with the Slim (just USB flash drives), and the older models and slim models use different hard drives.