I'm glad to see a lot of people on this thread understand the differance between current APS-C and Full Frame sensors.
For those that still seem confused just go get a current full frame camera and go home happy with your sharp pics while pixel peeping ok
now please stop posting in this thread.
For the more inquisitive minds trying to answer the topics question "Is Full Frame sharper than APS-C?" First it's important that you understand when comparing images captured on 135 (it's not 135mm btw, it's just the cartrige size used for 35mm Photo film, I just find it easier to type "135" rather then "Full Frame 35mm") to images captured on APS-C (Advanced Photo System "Classic" created in 1996 "for High-Resolution photos") it's not the physical size of the sensor that matters it's the physical size of the individual pixel sensors that need to be compared. So the question should REALLY be, "Are bigger pixels sharper than smaller pixels?" the short answer to that is no but that depends on how you use it.
For example, there is no point to compare 2 pictures at 50mm and at 35mm that were taken on the same camera; if you crop the 35mm to the FoV of the 50mm and blow it up to the same size as the 50mm than it will obviously be softer because they both had the same individual pixel sizes and therefore the same "resolving" power, one just got blown up to 150% compared to the other at 100%.
Back in the film days the grain size was tied to ASA speed (aka ISO), smaller grain (or faster ASA) also meant sharper finer details. In Digital photography there is no grain size, we now have pixel size and it is not tied to the ISO speed anymore, it's tied to resolution and sensor size. Current APS-C cameras have smaller/finer individual grain/pixel sensors than their 135 counterparts, think of it like the D800 vs the 5D3, so you need to compare them by "pixel size" not sensor size. Unfortuantely lenses made to be sharp on 135 don't care about resolving enough for the finer pixels of new APS-C sensors, this is why Canon is updating all their lenses. We are reaching a point where the lenses are becoming the bottleneck to image sharpness.
Of course smaller pixels have other issues such as light-gathering and dynamic range but new technologies such as gapless microlenses and back illiminated pixels are helping to boost these issues.
Oh and thanks for pointing out the 1Dx doesn't have a crop mode, I missed that, but the 1Dc video and Nikon Full Frame cameras have crop modes.
"...The 1D C offers 4K (4,096 x 2,160 pixels) video capture with an APS-H crop. You can also opt for a Super 35mm crop mode, ..."