Both...
...since it all depends on the character and most of all, on the campaign. I prefer really story-heavy, role-heavy RPG'ing. But sthat's so heavily dependent on the person running the game, and the number of players. Complex individual storylines --which have to be 'given' by the DM-- are so hard to pull off in large, or even mid-sized groups. I try to find a style of play that matches the game as a whole.
But its usually not so clear cut a line dividing 'power' and 'role' characters. And its best when its none at all.
I have 2 active characters in 2 seperate campaigns. My first, a 2nd ed. fighter, Lt. St. Jon Grod, is from look a pure 'power' character. A 7'01' half-ogre wielding 2 longswords with weapon mastery, with heavy armor and near max HP's. However, I always speak 'in character' during play, with accent. He's the least educated character in his unit --military campaign-- and it shows in play. He ignorant of anything non-military, distrusts magic --even when its helpful, until recently he blindly followed orders from superiors. The other players know him by what he says and the way he says it... not by his combat bonuses or his kills. So he's both.
My namesake Mallus Dargentum is 3rd ed, has 2 levels of the NPC class Aristocrat --which we beefed up slightly--, is a somewhat former drug dealer and would be courtier. He's far more 'role' on the surface, but he's as min/maxed as any 'power' character in terms of his field of expertise --diplomacy and deception. I tried to push the rules as hard as I could to create a ruthlessly charming bastard. So again, both. But I play him in a game with ample opportunity for solo play, to which he is well suited.