The big problem tended to culminate in per-pixel rendering which was really slow on Amiga (with planar bitmaps) and really fast on VGA (writing one byte per pixel).
Theoretically there was no difference as you could, ideally, just rewrite your renderer to render in planar modes directly instead of rendering to chunky (per-pixel) modes and then converting to planar. And chunky-to-planar converters eventually became quite fast but it was too late and nevertheless an overhead.
Amiga did quite fine until 3D graphics. "Modern" games like Dune 2, Syndicate, UFO: Enemy Unknown, Settlers, etc. were hugely popular but still complex games, yet playable, and no less good looking on Amiga than on PC. But then Wolfenstein, Doom, Descent, and others with full-screen 3D graphics with texture mapping happened and Amiga just couldn't even start the race.
If Amiga had had a chunky graphics mode it would've certainly had a few more years until complete technical obsolence. Commodore basically had that chance with Amiga 1200 with the new AGA graphics chip but they chose to extend bitmap planes instead.
For anything else, Amiga was competitive despite the lack of cpu power. I remember the last years of my personal Amiga use. Productivity software, editors, programming etc were still snappier and a much more friendly experience on the Amiga even if PCs at the time had 10x the cpu speed and Windows software was maturing up (and subsequently getting bloated beyond all usability).