Should I stop to hand-sharpen my chainsaw, or bring extra chains?
When you're in the woods, you probably want to spend your time cutting, not doing things you could do back in your shop (or have the hardware store do for you). So I would bring at least at least an extra chain: as many you think you'd need, plus one.

With an extra chain along, you are additionally prepared in case one has a problem that sharpening can't fix.

Hand-file sharpening is a useful skill. If you learn to hand-sharpen your chains, you can do that to all the chains at once back in your garage.