There's also the consideration that, at higher levels, the base dice of damage for a weapon isn't as big of a contributor. Consider a Monk with Str 14 (for a +2 bonus). If he/she opts to use monk weapons and dual wield, at sixth level (the lowest level where the armored monk can have all the relevant proficiencies), the character is at +3/+3/+3 (+4 BAB, +2 for Str, -1 for Flurry of Blows, -2 for dual-wielding with a light weapon in the offhand) to hit, and each hit with a mundane weapon will deal 1d6+2 damage, or an average of 5.5 damage. Our armored monk's best option for a weapon is arguably a greatsword, with which the character would be at +6 (+4 BAB, +2 for Str) to hit and deal 2d6+3 damage, or an average of 10 damage; this is 1/3rd the number of attacks, +5% to the chance to hit, and a bit under x2 to damage... which is unlikely to be worth it. The break-even point is a foe who needs a natural roll (for the first monk) of between 16 (where the first monk deals 82.5 over 20 rounds while the armored monk deals 80) and 17 (66 vs 70). That analysis does ignore the increased chance of a critical hit for the armored monk; with that in play (basically just multiplying average damage by 1.05 for the normal monk - representing a 5% chance of x2 damage - and by 1.1 for the armored monk - representing a 10% chance of x2 damage), in which case a foe who calls for a natural roll of 16 takes an average of 86.625 from the first monk and 88 from the second. But, by 6th level, the characters should probably be using +1 if not +2 weapons - for +1 weapons, the first monk is better off so long as the foe calls for a natural roll of 17 or lower if not factoring in crits (16 or lower if you are); for +2, 17 or lower either way. At 20th level, the first monk (assuming he/she has kept up on the relevant Two-Weapon Fighting Feats) is at +15/+15/+15/+15/+10/+10/+5/+5, while the second one is at only +15/+10/+5, and with the two likely using +5 weapons (possibly +5 weapons with an additional +1d6 elemental), the average damages are 10.5 and 15, respectively (or 14 and 18.3, respectively), meaning the first monk is going to markedly outperform the second (the second can regain a bit if using a Keen weapon, for a 20% chance to crit, but that doesn't really help much).

For armor, at 6th level, the first monk probably has Bracers of Armor +1 while the armoured monk probably has Full Plate +1 (they may each have +2 instead, that doesn't change things, really). Assuming Dex 12 (note the first monk would actually need a minimum of DX 15 to be dual-wielding, but we'll ignore that to make things as helpful to the armored monk as possible, seeing as his armor only allows for a +1 from Dex) and Wis 16, this means the first monk has AC 16 (Touch AC 16, Flat-Footed AC 15, Touch+FF AC 15), while the armored monk has AC 20 (Touch AC 11, Flat-Footed AC 19, Touch+FF AC 10). The first monk can move 30 yards per Move Action and runs at x4; the second is at 20/x3. The first monk also has no armor check penalty on skills, while the second suffers a -5 to such while also having to deal with an extra 50 lb of encumbrance. Probably overall an advantage for the armored monk, but not extremely so (he/she can't really sneak around and the like, and is pretty hosed against Touch attacks). But then at 20th level, when the first probably has Bracers of Armor +5 (possibly more, as those can go up to +8, but we'll ignore that so we don't need to worry about the armored monk running around in adamantine plate +5) and the second probably has Full Plate +5, the first monk now has AC 23 (Touch AC 23, FF AC 22, Touch+FF AC 22) while the second now has AC 24 (Touch AC 11, FF AC 23, Touch+FF AC 10). The first monk has move 40/x4, while the second still has 20/x3. I'd say that's an overall advantage for the first monk, particularly considering we aren't accounting for magic items that boost Wis and/or Dex (which the armored monk doesn't get an AC boost from, but the first monk does), or the +1 to 1 stat every character gets every 4 levels.

EDIT: A deeper dive into the SRD reveals that, first off, Wisdom isn't that big of a deal for a monk - it adds only to AC and to the DC of Quivering Palm. Secondly, dual-wielding requires you to start with high Dex and continue to build it up - the three levels call for DX 15, 17, and 19, respectively. So, an armored monk probably wouldn't bother with Wis and would favor Str. A dual-wielding, unarmored monk would probably want decent Wis at least to start out, but would focus on Dex and grab Finesse (considering most Monk weapons are light anyway; personally, as DM I'd allow Finesse to work with the quarterstaff for a Monk - think of it as the quarterstaff normally being simple, but an exotic proficiency lets you use it with Finesse and that's the version of proficiency Monks have). Say, our armored monk has Str 16, Con 14, other stats at 12 or lower (Dex 12, at least), and adds +1 to Str every 4 levels, while our dual-wielder has Dex 16, Wis 14, other stats at 12 or lower (Str 12 at least), and adds +1 to Dex every 4 levels. The armored monk would have a bit of an advantage at lower levels - at level 6, the character would attack at +8 (assuming a +1 weapon) and deal an average of 11 damage while having AC 20 (Full Plate +1), ACP -5, and move 20/x3; while the dual-wielding monk would attack at +5/+5/+5 (still assuming +1 weapons) and deal an average of 5.5 while having AC 17 (Bracers +1) and move 50/x4 (I messed up when the Monk gets improved movement, previously, as well as how much) Of course, looking still further, it looks like monks generally shouldn't even bother with any weapons - at level 6 an unarmed monk (who can still benefit from Finesse and Two-Weapon Fighting) deals 1d8 when striking unarmed, and in fact at level 20 this jumps up to 2d10 (it gradually increases as level goes up; at levels 12-15, it matches the greatsword's 2d6). Grab an Amulet of Mighty Fists of an appropriate level (giving between +1 and +5 to attack and damage rolls to unarmed strikes), and at high levels the unarmed monk will readily outperform the damage of one wearing armor and using a decent weapon. I'm honestly not entirely certain why a Monk would bother using Monk weapons...