Since both are hyper-threaded quad cores here's the basic breakdown, some of which you already know ( and I'm sure mal will correct me if I'm wrong, and I welcome it. )
The 3820 has better ALUs than the 2600K, so arithmetic ( including encryption, ) and heavy number crunching ( including rendering, ) will be substantially improved. It also supports quad-channel memory with faster rates, so memory intensive tasks will be accelerated. If you're constantly throwing heavy tasks at this machine and it's important that it get done as soon as possible, then the 3820 may be the way to go.
However the 3820 is an all-around more expensive platform, and this particular model can't be overclocked ( if that's important to you. ) Not only is the CPU more expensive, but the mboards are much pricier, you need quad channel RAM kits, they require more electricity to run, and you'll need to buy your own CPU cooler. You may have already been planning on aftermarket cooling, and if you're doing heavy rendering you may want extra RAM anyway, so those two points may be moot. However you're not going to get around the extra cost of the CPU and mboard ( the cheapest LGA 2011 boards are around $200 and that will get you a very nice Z68 board. )
I think you already know that neither CPU will offer an appreciable difference in casual computer use in gaming, so I won't go over that.
In the end, like mal said, it's what your budget dictates. It's hard to put a $$$ value on your time, so if you want to throw heavy rendering on this thing and have it done as fast as possible, the 3820 may be worth the extra money to you ( and you may decide that a 3930K is even worth it for the extra cores and overclocking. ) But if you're on a budget and you just need a solid machine that can crunch numbers for hours on end but doesn't ahve to be the absolute fastest, the 2600K may be better for you.