Grizzly bear: From http://www.animalstown.com/animals/g/grizzly-bear/wallpapers/grizley-bear-wallpaper-02.php
I’ll attempt to answer the second of these questions first. Since most of us consider vision to be our primary sense, the comparison with olfaction is distressing, and perhaps a bit controversial. Despite the fact that some display mavens say we see 16 million colors (on the basis of eight bits times three channels of color), cynics add “most of which are black.” The problem of counting discriminable object colors is a bit tricky, as many have noted. In general one counts colors by finding a perceptually uniform color space, delimiting the object-color solid in this space, and finding the volume of the object-color solid as the number of 1-JND cubes that can be packed therein. One number that seems to bear some authority is 2 million colors , but note that even the title of the article  attests to the trickiness of the assessment. For one thing the assessment is done in CIECAM02 space, which is arguably not perceptually uniform.
The number 2 million is paltry compared with a trillion, so either we are under-using our noses or we are counting wrong. I subscribe to the latter idea. When comparing the senses, you have to make sure you are counting the same kind of thing. For one thing we have binocular vision, but when you denote a trillion odors, you haven’t got other odor sensors that give you other dimensions (such as, say, two noses that give “bi-nasal olfaction”). More importantly, spatial vision has no counterpart in olfaction. So to be fairer to vision, you have to multiply the number of object colors (say 2 million) by the number of LMS cone triplets, which is about 2 million . This may give too much advantage to vision, because the number of fibers in the optic nerve is only about 1 million , which reduces the spatial address number to only about 300,000. Assuming each of these spatial addresses sees 2 million possible colors, the estimated total number of visual inputs is 600 billion---comparable to olfaction, but not exceeding it.
It appears that vision loses to olfaction by more than just “a nose”. And (returning to the first question) beware of the grizzly bear.
1. Bushdid, C, Magnasco, MO, Vosshall, LB, Keller, A. Humans can discriminate more than 1 trillion olfactory stimuli. Science 21, 343, 6177 pp 1370-72 (March 21, 2014).
2. http://www.grizzlybay.org/LearnMore/GrizzlyBearNose/GrizzlyBearNose.htm, accessed 27 Jun 2014.
3. Masaoka, K, Berns, RS, Fairchild, MD, Abed, FM. Number of discernible object colors is a conundrum. Journal of the Optical Society A 30 (2) 264-277 (2013).
4. http://www.wdv.com/Various/Eye/EyeBandwidth/index.html, accessed 27 Jun 2014.
5. http://faculty.washington.edu/chudler/facts.html#sensory, accessed 27 Jun 2014.
Michael H. Brill