It's simple physics. If you have 24 million pixels crammed on a aps-c sensor those pixel must be very small and therefore each pixel well will collect less light resulting in more noise. Sure it might be theoretically able to resolve more detail but in reality it wont as any detail will be smudged by noise as the processor is now making up values for the insufficient light. You can't add light that wasn't there to begin with. The 1DX will have the advantage as the pixels are larger, collect more light and the process produces a much more accurate image. In the real world this means better image quality and sharper images.
That is only true if you assume the exact same manufacturing process is used for both APS-C and FF. Manufacturing processes continually improve, as do the peripheral technologies related to sensors, such as the quality of the IR Cut and Low pass filter stack, CFA design, etc. If Canon is really doing something revolutionary with the 7D II sensor, especially if they apply some kind of active cooling mechanism to reduce dark current noise (which can eat up a fair amount of photodiode charge capacity), there is nothing to say they could not actually achieve similar light sensitivity characteristics with a 20-25mp APS-C sensor as they can with a 25mp FF sensor. Probably wouldn't be exactly as good, photodiode area is definitely a critical factor, but it is not the sole factor. I am not sure if Canon will take things that far, but it is not out of the realm of possiblility, actually it is well within the realm of possibility.
I can't say I believe any small-pixel sensor could perform as well as the 1D X. It has very large pixels that support a FWC of over 90,000 electrons. The 5D III is around 60,000 electrons. A 25mp FF sensor would probably be around 40,000 electrons. I could foresee an APS-C reaching into the 35,000 electron range if dark current is controlled with very efficient active sensor cooling, a 180nm process, and a very forgiving CFA...and such a sensor produce CONSIDERABLY better IQ than the current 18mp APS-C sensor (which scrapes by with a 20,000 electron FWC).
There is also the fact that smaller pixels divide detail more finely. On a per-pixel basis the standard deviation of noise might be higher, but from a whole-image standpoint (assuming you utilize all the pixels the sensor has to offer for each camera you are comparing), having more pixels can only be a good thing, and the average appearance of noise will be lower, not higher.