It's got a better codec and bit rate, at least on paper. Also, it's a new sensor (and better, if Canon are to be believed).
It can also shoot 12fps RAW. If most of your work is 'steady' without moving objects, you could even use re-timing to 'fill' in the rest.
We're talking about two cameras that nobody that is unsponsored haven't been used in paying production yet, so what the final look is anybody's guess.
In regards to the 1dx, Canon says it samples off the complete sensor (no line skipping like the 5d2) and greatly improves moire, which is a real issue with the 5d2.
The 1dx also is a much larger sensor than the 300 which can change plans when it comes to lenses, especially if you want to use PL mount lenses because you'd have to remove the mirror and most PL's wont' cover 24x36 (though some will).
Probably the right move for a 1dx that you wanted to use mostly for video would be to use manual focus Zeiss lenses that cover the full frame and that we using a follow focus system or a focus puller, you don't have to worry about the canon still servo lenses that reset every time you rotate past the end point.
The 1dx also doesn't allow for any audio sampling through headphones, without running a cable out to a box.
So in reality the 1dx isn't really a dedicated video camera, but probably would be close if not equal to the 300 because I believe they have the same sample rates.
It's a lot cheaper at 7 grand vs. 20.
In regards to shooting a sustained 12fps and putting them in a NLE or either a sequence composite like cs5 extended and letting the software pull it to 24p, you can do that and depending on how you shoot, what you shoot, the steadiness you shoot to, it can look good or it can look choppy.
I've done a lot of fast 10 fps still to video projectshttp://www.russellrutherford.com/magic/
and the once kicker is the image will flicker, partly due to a slower frame rate of 12fps and partly due to the different synchronization of the light source vs. the frame rate, especially using practical lights like street lamps, etc.
If you have a still camera that will shoot 10fps to 12 fps jpegs, go shoot a series, drop them in fcp at .5 a second still import and then process out the clip. You'll see the exposure go in an out quite dramatically.
I've done it for the look and for a few projects it works well, but 12 fps stills will probably never make smooth video or film looks.
As far as the 300, until I see it used, or until I see it really worked in post processing at this stage I don't understand it. For 20k you can buy an original RED One, which is a much more tested and viable cinema camera that shoots a real 4k file, 4 audio channels, tons of lenses, mounts and accessories and has a fast and reliable grading suite to pump out dailies to final files in almost any resolution. Also the RED One doesn't change frame size as shoot 4k.
Or if you don't want to spend 20 large then there are prosumer video cameras almost as capable and a whole lot cheaper that do close to the same thing.
It all depends on what you shoot and what your future plans are.
P.S. Now we probably will buy the 1dx because it will work in parallel with our RED's as a high iso still camera that tethers. To me that is it's worth that and the fact we can use it as a small crash cam or car mount cam when we need to.