Resolution is an optical term, in my opinion not usable in audio.
Speaker engineering is way too complex to put into a one line answer, but I'll make an attempt.
The primary advantage of a larger coil is more area to dissipate heat, so higher power handling.
With proper engineering good quality can be achieved regardless of coil size. Some of the best vintage speakers use even smaller coils.
So the quality of the speaker is more important than coil size. Power handling is improved by a larger coil.
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