Starting location has fairly little difference. While Limsa does have the whole "literally can't leave until 15" thing going on, hitting 15 is arguably easier than walking between Gridania and Ul'dah for a new player.

The main impact it has is pre-15 content. Up until then, there's three different main questlines dealing with your home nation, before they all merge for your first dungeon and stay merged thereafter. Also, most of the sidequests outside of the city, up to level 15, are only available in your home town (More specifically, it's that most sidequests outside of town are unlocked by progress through the main story, and those are unlocked by pre-15 main story quests)