From the same generation of sensors, it is reasonable to expect that the full frame images will out perform the crop, as the sensor sites will be larger. This gives the engineers more with which to work, e.g. more photons and more area on the die.

But (and this is the reason I wanted to add another answer), for the last couple of generations, today's sensors and cameras have become absolutely remarkable. Ignoring DxO, pixel peeping, and other counting of angels on pinheads and paying attention to real use cases, i.e. on screen display and prints, even discerning viewers are going to have difficulty distinguishing well exposed photos from one sensor to the next. Crop/FF, Canikon/Pentax/Olympus matter far less than good composition and light.

I have an engineering background and it is easy to fall into rather meaningless discussions about various differences, which in truth have very little impact on actual images. In part because these things are measurable, we can debate them objectively, but it is far too easy to lose sight of what matters (and is much harder to objectively discuss), the final images.