With an Epson, can't speak to Canon, your paper choice is very important as it is tied directly to the ink loading. On glossy PLPP 260 (premium Luster Photo Paper 260) tend to load the most. This was evident way back when Bill Atkinson created his custom profiles for the 11880 and 9880. He created a series of profiles for printing on canvas with Photo ink, and each called for a paper setting of PLPP260. If you did not use this, and picked a different paper, then ink load was not the same, mainly in the blacks.
All of Epson's profiles will tell you the recommended paper setting and if you create a custom profile it's important to note the paper setting you are using.
With canvas on Epson, with (7900 generation) the canvas media setting controls ink loading and the actual media, helping to maintain the correct running length of your canvas, the other media setting commonly used WCRW (water color radiant White) will lay down a lighter ink load and not control the running length.
A good test, is take a smaller print and try it with a profile calling for a certain media type, make 2 prints. One with the correct setting, one without, and see it you don't notice a difference in output. Sometimes, it's a very small difference, others, quite noticeably.
Example, if you print on BC Crystalline, (glossy canvas) with the canvas setting, and then make the same print with WCRW, the print with WCRW will look washed out.
I did not realize just how important maintaining the correct paper/media setting until I started to create custom profiles where I could a bit. Epson most definitely allows for different amounts of ink loading based on the paper/media setting.
Paul