Which is better, a chef’s knife or a serrated knife?

Yes.
As an all-purpose cooking knife, a decent quality Chef’s Knife is hard to beat. Yet some people prefer serrated knives of all kinds as their ‘daily drivers’ for cooking. There are even some companies that make serrated knives with a blade geometry very much like a Chef’s Knife.
For some applications, even in a culinary context, a serrated knife is actually more suitable. Like cutting bread with a relatively hard crust and soft interior, or cutting frozen foodstuffs.
If, for whatever reason, you absolutely can’t (or can’t be arsed to) maintain your knife’s edge at all, a serrated knife of any description will likely stay sort of useable longer than a straight-edged kitchen knife (also of any description).
If you want or need a really cheap, sort of useable all-purpose knife, a large serrated knife from one of the cheap ‘industrial’ lines of the major manufacturers might well actually be more useful than a ‘chef’s knife’ in the same price range. Mainly because a large straight-edged knife that will take a good edge, and hold it for a little while, needs to be made from fairly decent, not too thin, carefully heat-treated, steel, and those lines aren’t, generally. In a serrated knife, that doesn’t matter as much.
If you are mainly cutting thick-ish ropes, seatbelts, webbing and the like on a daily basis, an aggressively serrated knife will be a good idea, since it cuts those kinds of material very well, and will not get dull after a few cuts through those, like pretty much any straight-edged knife will. If that’s only part of what you do, a straight-edged knife with a serrated section of blade might be a good compromise (but for those kinds of application, you’d probably not consider a Chef’s Knife, or any other knife intended for culinary use).
TL;DR:
A Chef’s knife, except for when it isn’t.

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