If we look at epic weapon specialization with the +5 enhancement we are then looking at a strength score of 44 for the two-handed to win on average. Easy for an RDD, but otherwise the double weapons will often win damage-wise as long as they are heavily supplemented with feats.
Let's break this down and look at a standard fighter/wm that has 34 base strength with another +12 from gear for 18 modifier total. Let's assume the fighter will hit 75% of the time on his highest attack with a 2H and we'll compare greatsword to double sword.
Let's assume +7 weapons with 2d8 bonus damage to start.
2H = 7 (base) + 9 (bonus damage) + 7 (enhancement) + 6 (EWS) + 27 (strength) = 56 damage per hit.
Hits per round is 75%/50%/25%/5%/75% = 2.3. 2.3 * 56 = 128.8 damage per round.
DW: 4.5 (base) + 9 (bonus damage) + 7 (enhancement) + 6 (EWS) + 18 (strength) = 44.5 damage per hit.
Hits per round is 65%/40%/15%/5%/75 = 2.0. 2.0 * 44.5 = 89 damage per round for main hand.
Offhand is the same except for 9 less strength damage per hit, so 35.5 damage per hit. HPR is 65%/40% = 1.05. 35.5 * 1.05 = 37.3.
37.3 + 89 = 126.3.
So they're about even with that set-up (dual-wield slightly less) -- except that dual-wield requires 3 extra feats and does less damage per hit.
...and a 1H/shield has 102.3 damage per round output So in this case the 2H (or dual-wield) has about 25% more damage best case and loses all the shield AC.
In my playing experience, the survivability benefits of a shield pretty much exceed any benefits provided by 2H or double weapon.
In my own module, I did a few basic things to make 2H and double weapons more playable. 2H get enough damage bonus to give them double their STR modifier. Equiping a double-weapon or quarterstaff gives +2 shield AC and can be improved by +1 for every 10 parry skill points. I also reserve the best weapon enchantments for larger weapons. I won't argue that this is balanced, but it's made these options more viable and fun for me.
I'd certainly argue it's more balanced, at a minimum. By default there's basically no real reason to not use a shield, gain so much defense and lose little offense.
One of them is exactly what you were sceptical about: no damage immunities granted by items (they are OP to begin with due to possibility of stacking, then we have what you said about their value being ridiculously low for how powerful they are).
Er, I was saying the reverse, that getting like 10-15 damage resistance to a damage type barely takes up anything on the item budget. 10% slashing immunity makes an item require level 6...while 10 slashing resist only requires 5 and 15 slashing resist only requires 7. Once you get to higher values it's more reasonable (slashing resist 25 and 75% slashing immunity are about the same value) -- but except for critical hits the resistance is still much better at appropriate levels (would need to deal 34 average slashing damage per hit to make the immunity superior).
I, on the other hand, am under impression that ILR is quite a nice guideline after considering some anomalies like the above one. Well, at least on lower levels, because on higher ones the evaluation of items does get crazy.
Not really.
Take regen, for example. Unless you're going for a module with barely any healing then it's insanely overpriced in terms of budget. Regen +3 is a level 13 item...and it's equivalent to drinking a Cure Serious Wounds potion every 30 seconds. Cure Serious Wounds is valued at 66g while an item with Regen +3 is valued at about 33,600g. Usually going to be better to have 509 Cure Serious Wounds potions over an item with that regen -- among other things can burst heal when needed. And it looks even worse if we bring in full Heal potions.
Or the damage resistance as mentioned above, insanely cheap to sneak on 5/10/15 damage resistance which has a major impact.
Or how enhancement is cheaper than AB/damage. Weapon +4 is about 30k. Weapon with 4 AB and 4 bonus damage is 41k.
Or how having two items with 2 regen/2 saving throws is superior to one item with 4 regen and one item with 4 regen (by about 10% item budget).
So, yes, in epic levels it gets completely ridiculous but it still has major issues at low levels as well.
Edit: In case it interests you (all characters were humans, so no size modifier applied), 1H/S character had 44AC, 2H and 1H/1H had 35AC alike. Don't remember AB though, and can't check it at the moment, so this info alone is pretty much useless right now.
You've mentioned +5 weapons, so let's assume, say, only +6 strength from gear to be generous. Level 40 typical fighter has mundane AB of 46, so 54 in this case. Your AB is 10+ more than AC, which is kind of a problematic situation. In such an environment a shield doesn't do very much because you're basically going to hit most of the time anyway.