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How can I compare two different neural networks, from a theorical point of view?

Let's say I have a problem (i.e. Given f(x), find x) and two neural networks(i.e. feedforward and recurrent). I would like to know if one works better than the other one. I could run the twos on a computer, but other programs might interfere and I wouldn't know if the implementations I'm running are really the best ones humankind could create. Moreover, how could I be sure that the feedforward network worked better than the recurrent, when it might have just been "lucky"?

So, here is the question: can I compare the efficiency of two neural networks(with known sizes, structures and functions) from a theorical point of view? And if the answer is yes, how?

Thank you in advance.