It depends on how your sharpening kernel works, if it just enhances the contrast either side of a boundary like an unsharp mask filter then you want to use the YUV (or LAB) space but apply the filter on the luminance channel only.

The reason for this is that increasing the contrast of a colour boundary can result in odd looking colour shifts, i.e. in a pale red to pale blue boundary you could end up with yellowy-red line on one side immediately next to a strong blue line. Here's a somewhat extreme example (but using a real image. Can you guess the landmark?)

unsharpened image

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all colour channels sharpened

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just luminance sharpened

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Also you rarely see fine colour detail in images that's worthy of sharpening. Bayer interpolation / image compression both smooth colour detail. Also the eye isn't very sensitive to missing colour detail anyway (which is why compression removes it).

So in summary sharpening all channels will be three times the amount of work, can introduce colour artifacts and if not it may make little difference as there is generally much less colour detail than luminance detail.