I've taken some great images with my 5D Mark II. But I've also taken some great images with a Rebel XTi/400D. I've also found that it is easier to get great images and to get more of them in certain situations with a 5D Mark III and the improvements it has over the 5D Mark II than it was to get them with the 5DII.

I still use my 5D Mark II regularly, but only in ways where its weaknesses don't matter (e.g. with the widest angle lens I am using in a multi-camera setup). There are other cameras that have been introduced since the 5D Mark II that are even better. The 5D Mark II is a great camera, but the AF system is slooowww, inconsistent from shot-to-shot, and it has trouble focusing in very dim light - sometimes the same light in which the 6D and 5DIII can focus. Image quality is outstanding, but the 6D and 5DIII are both better in terms of IQ and AF.

If you've been shooting with your 600D "forever now" and plan to use your next purchase equally as long then you should probably consider a more recent model that can last you further into the future.

The replacement 5D Mark III was introduced in early 2012, so the newest 5D Mark II bodies are at least four and a half years old. The oldest copies that were sold when the 5D Mark II was introduced in 2008 are now eight years old. Many used copies of the 5D Mark II have got a lot of shutter clicks on them. I used mine for three years as my primary camera body and put over 60,000 shutter actuations on it before relegating it to a backup/2nd body role when I bought a 5D Mark III.

If you are absolutely bound and determined to buy a used 5D Mark II and you manage to find one in good condition then it will be a step up from your 600D. But for just a bit more a used 6D or even 5D Mark III would be an even bigger step.