Yes their is advantages,
1. Everything should look neater, more natural and prettier because it will be less "square" which is very unnatural. Not that a hexagon is a natural shape either

, but atleast its not uniform in design.
2. Movement, before you could have ships and land units crossing in the same spot.
I.e in a 4 square box (4 tiles in a square) the top left being water, the top right being land, the bottom left being land and bottom right water, you can cross both naval and land units over this junction, which is impossible, accept for tidal bridges which aren't in the game.
The hex's will cut diagonal moves out, so this removes this occurance.
3. Diagonal moves on a square grid is the fastest way to get from one end to the other. This is removed in the Hex grid with each move only possible to joining hex's no "jumping" as moving diagonal is effectively.
This also as others have said improoves strategic placing, less units are being used in civ5 at one time, and with 1upt you might struggle to hold an efficient front with square tiles, also move sides equals more ways for an enemy to attack.
All in all, Hex's will bring some benefits to the game.