I think this post really gets to the essence of the necessity for both "balance" and "variety" between characters:
I'm seeing a lot of excluded middle here between "everyone is just as good in each of the three areas" and "everyone is a specialist in each area and awful in the other two."
My only criteria for "balance" have always been
1) Everyone has something useful to do in all almost all situations
2) Everyone gets some spotlight time when they get to shine
It's entirely possible to follow these while, frex, having a thief be good at stealth but weak at combat. As long as the thief gets _something_ useful to do in combat (even if he's not a star here like the fighter is) and as long as he gets to be a star in stealth/exploration, it's fine. It's then the DM's job to arrange the encounters so everyone gets a reasonable amount of star time.
Mechanical "balance" then does not mean that all characters contribute equally to a (combat, skill, social) encounter. It means that characters have an equal opportunity* to shine throughout the narrative of a session / adventure / campaign, while still feeling important and part of the team when they are not shining.
In order to back up "having fun in the game" players have to feel both "balanced" and "different".
Balanced in the sense that a cleric is not, in general**, a better fighter than the fighter and the wizard a better manipulator than a socially specialized rogue.
Different in the sense that not all characters are created equal and are good in overcoming any type of challenge. This is a good thing because it creates character variety and encourages team work.
In order to create balance and difference between players, we need not only fluff, but also mechanics to back up this feeling in play.
I would argue that "balance" is diachronic rather than synchronic. This means that the feeling of balance should emerge after a certain time of play. Ideally this would be within the time frame of one session of play, but within the context of a broader adventure or campaign there are entire sessions where one character is shining more than others.
From this perspective, judging balance between characters synchronically, i.e. on the basis of a single encounter, is in most cases impossible because no single encounter can contain all different levels and domains of play and will inevitably play more into the strengths of character X than Y.
To a large extent this feeling of balance is created by the DM, who creates narrative opportunities for players to let their characters shine. But the ability of players to actually use these opportunities and stand in the spotlight is determined by mechanics. Mechanics should support the ability of all characters to do something relevant in any circumstance, while at the same time ensuring the ability of all characters to be generally "the best" in specific circumstances.
This means that mechanical variety and difference between characters is not a threat to balance, but a requirement.
To phrase it differently, characters should have some options which enable them to participate or contribute in each of the three pillars, but they should be better at one of the pillars, and perhaps "the best" at a subdomain of a pillar.
In summary: the DM should ensure that throughout a sessions, adventure and/or campaign equal opportunities exist for any player to put his character in the spotlight. This is the real balancing act of the game.
Mechanics ensure that (1) a player can make good use of this opportunity through the "difference" of his character and that his "moment" is not "stolen" by other players whose characters easily emulate the char's specialization; (2) that other players are not sidelined, but still contribute to the encounter.
* Of course, a DM can only create opportunities for PLAYERS. If a player chooses to play a "social" heavy character but is an awkward roleplayer, it's entirely possible he"misses out on his moments to shine. It's the same scenario with a player creating a fighter with a lot of tactical feats, but who isn't able to make good use of the battleground setup the DM offers.
** In general is a key word here. A cleric may be very well able to call on her god to grant her superhuman strength and beat the fighter on his own game - but this should be the exception, not the norm. A wizard succeeding in casting charm person *is* more effective than the rogue with maxed diplomacy skills, but this is not a continuous, reliable ability like the rogue's social talent.