For that processor they'd both be about the same. But at least the Gigabyte board has a heatsink on the VRM FETs so however small and un-finned it may be it's still better than the nothing that's on the Asus board's FETs. That said, neither should you ever plan on anything more than an 8 core CPU and even then only if not overclocking. Actually, it's probably best to not go above 6 cores on the Asus.
Both have USB ports, both have SATA ports, both have an NVME M.2 port, both on-board audio and on-board LAN. Neither support SLI of Nvidia GPU's.
So it gets down to how you plan to to use it: how many of those ports do you plan on using up? Does the Asus have enough (ports) to persuade you it's lack of heatsinking is worth it?