Why do you need a new one? Is it getting too slow? If so when? There's just not enough information.
I would do a two step process to improve speed:
You could also buy two additional sticks of RAM. Those are very cheap these days and your applications seem very demanding.
Keep the computer. Get an SSD then spend the remaining money on a new tablet.
Get 16GB of RAM (it's cheap at the moment), 1600 speed is good enough, and a large enough SSD, Intel 520 or Samsung 830 series. (Ignore the tablet comment, it's beside the point)
I guess the programs eat up ram and will benefit from more. Program startup is much faster from an SSD.
You can install these parts and see if it's fast enough. If you have or want to move to step two you can reuse these parts, no money wasted. Also this step is safe to do as it won't interfere with your current, running system in a major way.
Second step would be a mainboard and CPU upgrade (+ a mounting kit for the cooler. Email Noctua, maybe they'll send you a Socket 2011 mounting kit for free).
The maximum frequency for a new CPU from Intel is ~3500Mhz +-100MHz. That's just over 20% more compared to your old CPU. Usually an upgrade is felt when the CPU speed is increased 50%. With a Six core CPU raw performance will go up about 50%, but not many programs can use six cores (Photoshop does, the audio programs I don't know). The frequencies you listed are turbo frequencies, when NOT all cores are in use the remaining ones can speed up.
Intel i7-38XX series are the fastest and by far the most expensive CPUs. They need a mainboard based on the X79 chipset (also expensive). Some of these board have eight DIMM (ram) slots, so you can get up to 64GB of RAM. The X79/i7-38XX combination makes sense only for two scenarios: You need 64GB of RAM, because there's no other (easy) way to get it, or you need a six core CPU, the i7-3830 is the cheapest one. This mainboard and CPU will cost you 800$. I don't know about the particulars of the PCIe to PCI bridge issue, so I'm not listing it here. Feel free to do your own research.
The i7-3820 you mentioned has four cores and is barely faster than i5 CPUs for half the price.
The Intel i7-2XXX series and i5-2XXX series will be replaced within six weeks. If you don't need 64GB RAM or a six core CPU, you should wait.
The i5-3570K is what you want if you wait, 3.4GHz quad core with low power consumption. It goes into a mainboard with the Z77 chipset (or Z75 or H77). This CPU mainboard combo will be between 400-500$. The Asus P8Z77V
is pretty much the successor to your current board.
The Fractal Design Define R3
and Antec P183
are nice, quiet cases from the recommended list
with good cable management.