If skirtboard and baseboard are the same thing you can go either way. Personally would want to do the skirtboard/baseboard before carpet. You can raise the skirtboard/baseboard a 1/2" which allows the carpet installer to tuck the carpet under for a nice neat appearance and this makes painting easier in the future because you can slide a thin piece of plastic between the skirtboard/baseboard and carpet. If you decide to do the skirtboard/baseboard after the carpet be sure to ask the installer to compensate for this by moving the tack strips an extra 1/2" to 5/8" inch away from the wall. The problem if you do not account for the extra 1/2" it will make replacing the carpet in the future much more difficult because the tack strips will be under or too close to the skirtboard/baseboard.
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