I would say FRLG is the better remake. It's more of a remake then HGSS is.
Plus it has Leaf, the most win-filled character in all of gamedom.
HGSS has a lot of enhances. I would compare it to Harvest Moon: Back to Nature/For Girl and Harvest Moon: Friends of Mineral Town/More Friends of Mineral Town.
It's more of an enhanced port, though I still think of it as a remake.