It's a shame the Tiger is so powerful, makes getting any other UR feel like you're losing. Dragon of Echigo doesn't lean to any particular unit, does she? Currently got her as a Personal Guard because I had one handy and wanted another front defender.
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From the FAQ under Generals -- Main Attributes
Power: Generals with higher Power will deal more damage to enemy units.
Leadership: Generals with higher Leadership will take less damage from the enemy.
Intelligence: The power of some of the General Skills can be boosted by Intelligence.
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Oh, other than skills which specify it (like the Dragon), does who your party leader is affect anything?