I would use Espeon, personally. It has better offensive stats, which, for me, is better for a Pokemon used in game. Also, if you keep Haunter, Dark and Ghost hit the same types super effectively. I will say, Umbreon does have a slight advantage in being able to hit the Kimono Girl's Espeon super effectively, but thats about it. I'll go over how well Espeon and Umbreon work with your team, I will say I don't know a lot about HGSS so I'll go over everything.
-Covers Lapras's weakness to Fighting with its STAB.
-Covers Tyranitar's weakness to Fighting with its STAB.
-Covers Haunter's weakness to Ghost with Shadow Ball (though its also weak to Ghost type moves).
-Covers Ampharos's Ground weakness with Grass Knot.
-Arcanine can hit steel types with a STAB Fire move.
-Arcanine also can KO Bug types with a STAB fire move.
-Tyranitar can hit Bug types with a STAB rock move.
-Covers Tyranitar and Lapras's weakness to Fighting with Psychic.
-Covers Haunter's weakness to Psychic and Ghost with STAB.
-Arcanine can hit Steel types with its STAB, as well as Bug types.
-Tyranitar can hit Bug types with its STAB.
So, I would personally opt for Espeon, but either works, really.
Hope this helps! :)