Since I've been pondering the same question, I can give you some hopefully useful thoughts to consider.
First of all, let's assume that still photography isn't important for you. Let's also assume that money is not a deciding factor.
You can get your hand on a 5D3 nowadays for around $2500 (plus or minus $200 depending how much you like buying from eBay retailers). Add about $400 to that for a few CF cards and maybe another $100 for a couple of batteries. Total cost is within $3500 for a camera you can go out and shoot with.
Blackmagic 4K is $3k for the body, add another $350 for about 3 SSD 128Gb drives. Now here's the catch...you absolutely will need an external battery unless you're planning on only shooting indoors. So you really need to add $300-500 at least for that. Total cost is within $4000 for a camera you can go out and shoot with.
Dynamic range is roughly in the same ballpark, about 11 stops with maybe the 5D3 having a slight edge over the Blackmagic.
If you're planning on shooting in low-light conditions and with only available light, then the Blackmagic won't work for you. The ISO400 is not sensitive enough for anything less than a well lit indoor, or daytime exterior. You won't be able to push the footage in post without massive noise. If your bulk of shooting is nighttime, dark interiors etc, you will need the 5D3.
How important is resolution for you? 4K is much more future proof, but right now it's simply overkill unless you're planning massive re-framing in post.
The 5D3 full size sensor is both a blessing and a curse. I can tell you that most pro DP's despise it and much prefer the Super-35mm sized APS-C.
Both cameras can be reliable and unreliable. They both can suffer from dropped frames, with the 5D3 having a slight advantage in the sense that you can set it up to stop recording if frames are dropped (which is not possible with the Blackmagic).
Blackmagic has inputs for 1/4" audio lines, however the in-camera levels are poorly implemented and the build-in amp crappy. Still, it's a bit more "pro" than going into the mini-jack on the 5D3.
How important is it for you to use an external monitor? The Blackmagic monitor kinda sucks, especially in bright light. The 5D3 monitor is kinda small and annoying to pull focus, particularly with a full frame sensor. If you plan on using an external monitor with the Blackmagic, do know that you'll need one with SDI inputs which might push the price up (no HDMI out on the BMPC).
Lastly, how important is it to be inconspicuous when you shoot? A well rigged Blackmagic will look more "pro" than a handheld DSLR in public places.
Depending how important the above points are, should make it pretty clear on which camera you should buy.
P.S.
You will need a faster computer than what you have either way. Resolve is CPU and most importantly GPU hungry. I wouldn't recommend anything less than a 2012 model.
