Hi Bobsp,
If it helps here is my experience:
I went from a 40D to a 5D mk1, and was wowed by the improved image quality.
Full frame is great for portraits and landscapes, and also improved lowlight capability.
The only draw back for me was when i wanted to shoot motor sport as the 40D appeared to focus quicker and had a higher burst rate of 6fps compared to 3fps with the 5D, luckily though i was able to keep my 40D for these situations.
However in your case, the 5D mk2 has slightly better burst rate than your current 600d 3.9 compared with 3.7, so this would not be an issue.
Obviously if you are into motorsport photography or perhaps wildlife then the FF will not have quite as much reach as your 600D although the extra MP of the 5D may make up some of the difference if you wanted to crop.
The only real draw back that i can think of would be if you have a number of ef-s lenses as these will not work on the 5D and therefore you will need to invest in some new glass for your new body.
On the 5D you may see more vignetting using the same lens compared with that of your 600D and possibly softer edges due to the nature of the cropped sensor compared to fullframe, and is the reason why decent glass is a must to get the best out of a full frame camera.
Overall though you will, im sure, be wowed as i was by full frame photography if you decide to invest.
Cheers
Pete