That's a great idea, using both and doing your own test. I can tell ya just about what's gonna happen and why.
Please understand from the start, I'm not a closed minded MG hater, and they have some better products than they used to. Having said that, I have used MG on everything but weed, and know that it will make your plants grow rapidly, carry a deep, dark, nice color, and stack the flowers. The mushroom compost, is pretty hot for organic soil, but will prolly not outgrow the MG by itself. Using the mushroom compost, you would need to do alot of things to get a matching growth rate and yield as you would with the MG. that's for sure.
Here's where the true test comes in, and you WILL know the difference, when you smoke em' side by side. The stuff grown in the compost, will burn evenly, it will burn to a clean grey ash, and the last hit off a joint, will taste as good as the first one did. The MG, if not flushed, will not burn properly at all, will turn into a black nasty char in a bowl, and will not burn in a joint. If you flush it real good, it will burn better, but not nearly as clean as the compost grown, and the taste difference will be night and day, especially, the further down a bowl or joint you get.
Now, I know there are MG believers on here that will say that there stuff tasted fine, but believe me, side by side you WILL taste the difference, and you'll throw that MG in the garbage.