f stop depends on the focal length, and its for a good reason that they are great indicators of the light grabbing ability of a lens - the size opening of the diaphragm is useful for comparison only with respect to the angle of view of the lens (ie, the focal length)
"a 200mm at f/5.6 is way larger than a 50 mm at even /2.8" - while this is physically true, AFAIK, the smaller f numbered lens will be letting in more light (thus faster) IRRESPECTIVE of focal length (because its already taken care of inside the ratio)
Think of it as the circular cross section of a cone. While the area of the circle can vary depending on where you bisect it, the equations that describe the bounds of the cone dont - ie, the cone remains the same for a given f number - and therefore the light capturing ability too.
In short lower the f number, faster the lens, irrespective of focal length.
The 50mm f/2.8 is easily a few times faster than the 200mm f/5.6.
Thats what I know, if I am wrong I'll be glad to be corrected