Not quite, the C64 was (technically) able to display 16 colors at all times, even in 320x200. There were a few catches, though: in 320x200, it was only capable in displaying 1 color out of 16 plus transparency per tile which is referred to as monochrome mode. Most games used a 40x25 tile mode which meant that you could theoretically use all 16 colors on screen, just not everywhere you wanted.
In multicolor mode (3 colors out of 16 plus transparency per tile) the C64 was restricted to a resolution of 160x200 pixels, which meant horizontal pixels were twice as big. Most games mixed both modes for the best of both worlds. For example, in in Giana Sisters, the HUD, the clouds and the gems Giana collects are monochrome tiles while the rest of the game is multicolor, I think the game is still quite pretty today. There are also multicolor and monochrome sprites where similar rules apply. Multicolor sprites can have up to three colors but yet again, their horizontal pixels are twice the size than the ones of their monochrome "brethren".
As for the Amiga: I'd like to add that besides the PC, the Amiga's main competitors were the SNES and Genesis -- while the Amiga was pretty well-suited for the platform and action games that were popular at the time, the consoles from that era simply were a tad better at games like that. After all, their hardware that was specifically geared towards fast scrolling and lots of sprites while the Amiga was designed to be something like a Jack of all trades. Being outclassed by PCs when it came to adventure games, sims and 3D games and consoles when it came to action games and being faced with insane piracy rates, the Amiga was in a pretty difficult position in the early 90s.
There are a few pretty awful Amiga to Genesis ports, though. Amiga programmers liked to use gradient overlays to make their games look more colorful. This effect couldn't be pulled off on the Genesis due to its lack of transparency support and small color palette which is why the ports of games such as James Pond looked really drab on Genesis. Another major problem was the Genesis's sound chip which was vastly inferior to the Amiga's.
Of course, when programmers tried to port their games the other way, the results were often awful as well. The superiority of the Genesis couldn't be denied when it came to fast, multilayered scrolling. Plus, while the Genesis couldn't display the Amiga's fancy gradient effects and had a smaller overall palette, it was still able to display more actual colors
on screen than the Amiga which gave it an edge for more realistically-styled graphics. An example of how this leads to pretty horrible-looking Genesis-to-Amiga ports is a certain game a certain someone posting on this page named themselves after.
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