To summarize, yes, the 1Dx blew away my 1D3 by a mile. Both were 1-series high-frame-rate variants (no difference once you get to the 1Dx, but it was 1D vs. 1Ds back in the day of the 1D3), and it was only a 0.3x crop delta, not the full 0.6x of APS-C. It could have also been two generations of technological improvements, as the 5D3 didn't immediately jump out at me as magical, and we bought that one first, though admittedly it was a bribe to my wife ("here's a new camera. Hope you don't mind me buying a bunch of lenses now too.") and I didn't shoot much with it (still haven't). The 1Dx impressed me so much (moving from a 1D3/7D pairing to a 1Dx/1D3) that I bought a second 1Dx within 8 weeks, moving my beloved 1D3 from primary to benchwarmer in that amount of time.
Now, for the sake of mention, even though the 5D3 has the same AF sensor as the 1Dx, it doesn't have near the CPU horsepower (1 Digic vs. 3; 2 for imaging and 1 for AF/exposure), and IMHO this makes an appearance in how the AF works. To me, it's just not the same. I wasn't thrilled with it when I shot our dogs at the dog park with a 70-200/4IS (a fantastic performer IMHO), though again a disclaimer is relevant here: I was new to the menu options at the time. However, I found confirmation (and justification...) after reading this review: http://chrisgilesphotography.com/blo...g-photography/ and added a 5DsR to our fleet shortly thereafter. Wow. Just wow. I had been the strongest 1D-series addict known to my corner of the world for years, whether it be the build quality/feel in hand, control customization options (I was addicted to ISO on the big wheel, extremely useful in Av so the two sides of the triangle that I controlled were immediate knobs with no need for a button push prior), AF, IQ, whatever. Now, the 5DsR is my "first-alarm" camera for EVERYTHING unless bad weather, unpredictable sports, or a perceived need for an extra 1/3 stop of sync speed causes me to begrudgingly reach for a 1Dx. My second 1Dx has moved into my wife's bag to be her "long lens/action/high-frame-rate" camera.
So, not to turn you away from a 5D3, but do take a good, long, hard look at a 5Ds of one sort or the other. I'm still consistently blown away at the clarity and detail. Here's just one sample: I ordered a new softbox that's supposed to create a perfectly round catchlight (even though it's not round). I had a friend go along, set up the light, and took one shot (gosh I love TTL). 5DsR, 70-200/2.8IS (yes, the old model). I forget the EXIF but I think it's ISO 100, f/5.6 at 1/200th. I zoomed in on the LCD and said "You're wearing colored contacts!"...go ahead, zoom in on it: http://photos.templin.org/images/hexoval-102.jpg (yes, the lashes are fake too...I knew that already)