Just to make sure you know... you won't just be replacing the processor. You'd be replacing the motherboard as well. No, don't get insulted. I'm not assuming that you didn't know this. You didn't mention it, so I did.
What happens when you put a dedicated video card in a system with an integrated video card? Well... let's put it this way. Let's assume you choose Windows. You install Windows on a computer with an integrated video chipset/cpugpu. You install the drivers and get everything working nicely. You then decide to add a dedicated video card. So, you turn off the computer, you plug the card in the slot, you turn it on. What happens? Depending on the settings in the BIOS, either the card is automatically detected as the new primary, or it is ignored as the primary display device during the Boot sequence (since the onboard video was previously the primary). However, the BIOS won't automatically disable the onboard. Once you are back in Windows, you will now have two video adapters available.
You can go into the BIOS and disable the onboard video, which will free up any shared video memory. Right there is the main performance difference. The onboard video chipset will borrow some of your system Ram and make it unavailable to the rest of the system. Using a Dedicated video card will enable you to free that Ram up for the system.
It is up for debate whether the integrated GPU steals CPU/processing power. On the one hand, empirical evidence gathered while watching a CPU meter says it does, yet there is no documentation or benchmarks to back that up. As has been said, the only difference there between older integrated chipset motherboards and these new Intel/AMD chips is that the GPU is built into the processor, instead of the motherboard. The Processor remains as powerful as it is, regardless of whether you use the integrated video.
Which is better? Your Radeon 6800. By Far.
For what you do, having as much Ram as possible is always a good thing... so not losing any to Shared Ram is a good thing. Also, you'd see better performance in your 3D rendering program (not necessarily the speed of the rendering, but the display while you are working) with the Radeon 6800.