I had contemplated that very question too for quite long.
Canon took so long to release the 1Dx and the 5D3 came along much quicker. Having read the reviews of the 5D3, I jumped at it first and was very happy with it.
It does have more resolution at 22mp than the 1Dx, though not a big deal more than the 5D2, in other areas it was a jump in the right direction on many fronts.
The 1Dx was announced so much earlier, yet it took so much longer to reach the market, I just didn't know how shooting with one would be like.
The reason I got the 1D4 was because of its speed and reach (1.3x crop), which is good for both sports and birds. Imagine a 300mm f2.8 would equal a 390mm f2.8 withtout any converts and factor in the price of a 400mm f2.8 and its weight. While the 1Dx would be faster, to get the same reach would mean a tremendous strain on finances and a huge increase in weight. If the 1Dx came out earlier and at a more down to earth price, the result could be different today.
Of course there are drawbacks - the 1D4 v 1Dx: slower fps, not as good color, digic 5 vs digic 4, better focusing system, better low noise at high ISO (1D4 is about eql to 5D2), but on the whole, the 1D4 is a pretty damn good cam. Shooting with the 50L/85 it makes a great portrait cam. Focus acquisition is lightning fast. And with the 1.3x and 16.1mp, if you are going to take birds or bugs, that is equal to higher resolution per pixel. Its a different perspective from FF, which for a photographer is a good thing - the difference opens different angles/perspectives. Oh and I DO like the sound it makes when the 10fps goes off...lol