Cork is a good choice because of its insulating qualities; The Guide4Home points out the benefits of cork flooring: it's impermeable and provides thermal insulation for cold concrete floors, and this helps with sound insulation too. And it can also be used as an underlayment for this reason.
Carpet is also good. A carpet's pile is a good thermal insulator. On a concrete slab, surface temperature with carpet is much higher than the temperature on hard tile. And Guide4Home points out that "For insulating value, wall-to-wall carpeting constructed with a deep, dense pile having a ... dense padding serves you best." since the R value is affected by thickness.
But while both are good choices from a thermal insulation standpoint, as well as for sound insulation, other factors can enter into the buyer's choice. One important factor in both cases is the underlayment/padding, but your choice can be affected by the sustainability and the hypo-allergenic qualities of cork. The Guide4Home points out that "It has hypoallergenic properties and is resistant to moisture i.e. no chance of mildew or mold setting in".