The bit has little to do with how many colours can be supported - as is already said, 8-bit = 1 byte = 256 'possible' colours.
Bitplanes were what made the difference. For instance, a lot of systems used 4-bit bitplanes, so really that's 2 pixels per byte, or 16 colours. 2-bit bitplanes were often used on 8-bit systems, like the C64, but that was just the graphics mode. The 64 could support different bitplanes, and most 8-bit systems could support the Spectrum resolution, with just a pen colour and paper colour, so a 8x8 pixel area would have only 2 colours, but the colours could be changed per row and column. This lended itself well to platform games, a standard grid, that never did Manic Miner and countless others any harm. It also allowed for code portability. Without that mode, we wouldn't have had so many games on the 8-bits.
For me, I think artists are a bit spoiled these days, and actually find myself going MEH at glorious graphics because I know that there's nothing epic that takes several people and systems to do. It's not epic to make a model, it's their bloomin job, and the job of all the other people involved. I'm much more impressed by what 1 guy on their own can produce. It's good to know there are still people out there using reduced colour palettes, which I find more appealing than modern pixel work. Some of the pixel work in SNES RPG's is just incredible.
My own personal favorite style has to be the Bitmap Bros 16-bit games, they took 16 colours and made them work. In their day, nothing came close to the graphic quality. Most games in that time had their art done on the Amiga, which has a more standard 32 colours, but the Bitmap Bros always did a better job on the ST's 16-colours than other developers.