What has a greater effect on concentration? Dilution or an equilbrium shift?

It is not clear to me what the constraints are for stresses. Can you add any stress you want? I'll answer your question assuming you have full liberties.

If you think mathematically you could calculate the change for a few hypothertical situations and see which would be more. To compare you could calculate the % of the complex ion that breaks apart into the iron and thiocyanate.

If you want to approach it qualitatively you want to think about things like precipitating out an ion, removing it completely from equlibrium and see how far you could get the equilibrium to shift in the direction to replace that ion (this is usually limitless). Or you could add a common ion and see how that shifts the equilibrium to the opposite side of the equation.