The 20D was a groundbreaking camera when it was introduced. It was and is capable of making very good images.
Unfortunately, the term "crystal clear" when applied to photography isn't very specific, and could describe a wide range of issues with different causes and solutions. The photos you posted on your site are good - perhaps you can post an example of what you don't like, or maybe give some more information. Things that could cause photos to be what someone might call "not clear" would include out-of-focus images, camera movement during exposure, atmospheric haze, UV light at altitude, poor image processing, something wrong with the lens (like a misaligned lens element), a really dirty lens or sensor, flare from a bright light source in or out of the frame, flare from using a crappy filter, and the list goes on. Given the age of your equipment, it's quite possible that there is something out of whack.
Although the 20D and your lens are capable of good images when they are in peak condition and used properly, I'm going to suggest that getting a new camera would be a good idea -- even if nothing is wrong with yours. The last nine years have seen a major improvement in digital imaging at all levels. In addition, there is an entirely new class of compact cameras with interchangeable lenses, which provide outstanding image quality while greatly reducing the size and weight of your kit.
If you provide more information about the kind of photography you do, and how you approach it, you'll get some good suggestions on what you might look for in a new system. For example, if you shoot landscapes for large prints, and you use a solid tripod and careful technique, a Nikon D800 would work well. If you shoot travel or documentary photography, and want something small and discreet, a Sony NEX or an Olympus EM-5 or one of the Fuji X-Pro cameras would be a good choice. Given what you already have, I don't think that you have to stick with Canon for a system, though if you do a 6D with the new 24-70 or the older 24-105 would make a nice kit (not sure your current lens will mount to a 6D.)
Hope this helps.