The SNES came 2 years after Genesis and was more powerfull. It had a higher resolution, more colors, better sprite capabilities, more memory (2X RAM, 8X Audio memory) and way better sound (Doom SNES sounds better than Doom 32X). Genesis had a faster CPU, but that was all. Here are the specs.
Basically, Genesis could do games with things going crazy fast like Sonic better than SNES because of the big CPU difference. But in general visuals, SNES was considerably superior.
About people thinking its the opposite, it was because of Sega's way superior marketing. Nintendo had better specs, but the public, specially kids, would brag about numbers like RAM, sprite count, resolution, without even knowing what they were talking about. Then someone at Sega USA looked at the spec sheet and saw that they lost in everything, except the CPU. So they created the Blast Processing marketing effort to make it look like it was a different and advanced tech, instead of only more MHz. As you can see, it worked pretty well.