If you want to find out how different props load an engine then use the formula Diam^4 x Pitch. Which just means multiplying the Diameter of the prop by itself 4 times then multiplying by the Pitch.
In the case of your 13x4 prop you'd have 13x13x13x13=28561 then times 4 = 114,244. For the 12x6 prop the figure comes to 124,416 so that prop will load the engine just a little more than the 13x4.
Of course, this is only a reasonably accurate guide when comparing two props having the same blade shape etc...a 12x6 APC will load an engine differently than a 12x6 MA for instance.