I used to shoot with a 20D and I had exactly the same thoughts.
I think there are a few things going on here.
1. The camera is 8MP and when viewing files at 100% - it doesn't look as great as a 5DMK3.
2. If you haven't done so already, take a look at the picture profiles. The camera can be set up to pump out sharper jpegs with more contrast and saturation.
I tried this and was amazed at how much difference it makes. This of course can be done with RAW files in software.
3. Use the free DPP software that comes with the camera. It's optimised for Canon lenses and gives you the opportunity to make adjustments that are tailored to the hardware.
4. How big are you printing? Are you printing at all? Will you ever print?
A postcard sized print means we could all get away with using a smartphone. If you're showing in a gallery. Upgrade!
5. Lens choice is important. You don't have to get L series glass either. There are some inexpensive primes that are arguably better than some L zoom lenses. Primes are sharper and have more contrast.
I recently got sick of lugging around my 24-70mm 2.8 L lens and picked up the 40mm 2.8 prime. Now my images are so much punchier, clearer and sharper edge to edge. Check out this website for lens quality comparisons.http://www.the-digital-picture.com/Reviews/ISO-12233-Sample-Crops.aspx
The other secret weapon is the EF 100mm f2http://www.photozone.de/canon-eos/166-canon-ef-100mm-f2-usm-lab-test-report--review?start=1
Out of all the above - I really believe setting up the picture profiles makes a big difference. Play around a bit until you get the sharpness, contrast and saturation right and I think you'll find it makes a huge difference.