It is an either/or choice, as reputation controls the class of your hero. Once you have enough Blood points or Tears points, your hero changes class and gains a new ability. You then get the chance to fill the points bar a second time (but only with the same type of points), which gives you an advanced ability for your class.
As in previous Heroes games, each faction has a might based hero and a magic based hero. In Heroes VI, each faction also has a might or magic based Blood hero and a might or magic based Tears hero, for a total of six classes per faction.
Shamelessly stolen from the Heroes VI website, the following table lists all the hero classes available:
Haven
Name Type Reputation
Knight Might Neutral
Cleric Magic Neutral
Paladin Might Tears
Confessor Magic Tears
Vindicator Might Blood
Inquisitor Magic Blood
Inferno
Name Type Reputation
Heretic Might Neutral
Warlock Magic Neutral
Hellcaller Might Tears
Demonist Magic Tears
Chaos Lord Might Blood
Pyromancer Magic Blood
Necropolis
Name Type Reputation
Ebon Knight Might Neutral
Necromancer Magic Neutral
Bone Guard Might Tears
Embalmer Magic Tears
Death Knight Might Blood
Reaper Magic Blood
Stronghold
Name Type Reputation
Barbarian Might Neutral
Shaman Magic Neutral
Chieftan Might Tears
Earth Shaper Magic Tears
Warmonger Might Blood
Storm Caller Magic Blood
Sanctuary
Name Type Reputation
Samurai Might Neutral
Monk Magic Neutral
Shogun Might Tears
Tide Master Magic Tears
Warmaster Might Blood
Flood Conjurer Magic Blood
Best Answer
That's no pillar - it's a Blind Maiden! In combat, it functions similarly to its adventure map counterpart by giving any unit in the glowing square bonus Destiny (Luck from past games).
^This is the adventure map version.
Jason Berkan gives sound advice: right-click all the things to find out what they are!