So looking at these three weapons, I would like to compare the quality based on the RNG. I would like to ignore most of the other primary / secondary affix's for the purpose of this question.
Here's my guess and correct me if I'm wrong…
DPS = (Total Dmg Max + Total Dmg Min) / 2 * Attack Speed
Total Dmg Min = Base Dmg Min + (Elemental) Dmg Min
Total Dmg Max = Base Dmg Max + (Elemental) Dmg Max
Attack Speed is a constant value for an item (not RNG [ignoring +Speed% affix])
Base Dmg Min not displayed in item stats and is the true RNG base damage minimum
Base Dmg Max not displayed in item stats and is the true RNG base damage maximum
(Elemental) Dmg Min is an affix and RNG
(Elemental) Dmg Max is an affix and RNG
So my assumption is that DPS, Total Dmg Min, and Total Dmg Max are all calculated fields and not true RNG numbers on their own. Is that correct? That would mean the true RNG values are what I'm calling "Base Dmg" and "(Elemental) Dmg"
Based on that, the true RNG values for these weapons are as follows…
Total Dmg | Calculated | 3824-4446 | 3896-4573 | 3504-4077 (Elemental) Dmg | True RNG | 1739-2130 | 1870-2322 | 1767-2165 Base Dmg | True RNG | 2085-2316 | 2026-2251 | 1737-1912
So based on all of this analysis, I can come to the conclusion that the first one in this list is the best in quality because the Base dmg is the highest. That person could have rerolled the elemental damage to make a higher total damage than the second and third items ever could. (Though his reroll to +10% damage was probably a better choice, but that's not what I'm arguing here.)
Best Answer
The DPS, weapon damage range and attack speed listed at the top of the item tooltip, next to it's picture, are all calculated fields. Anything below that is an RNG number
Looking at the Diablo 3 Game guide on The Furnace (or any weapon but we're looking at this one since it is in your question. Take into account these are stats for a level 31 Furnace), you see that it's "base damage" and "elemental damage" are both RNG rolls. Notice that the left set of parentheses is the minimum damage roll, and the right set is the maximum damage roll.
To get the weapon's calculated DPS, the game will take both the base min-max and the elemental affixed min-max roll and add them together, then multiply them by the 6-10% damage bonus if there is one (also giving us our listed damage range), and then multiplied again by the listed attack speed (If there is a +% attack speed stat, it will automatically figure that onto the listed attack speed for the item at the top as well). So we end up with:
((((base min + elemental min) * +% damage) + ((base max + elemental max)* +% damage)) / 2) * weapon attack speed
The tooltip DPS will not include any socketed emeralds, but will include socketed rubys which would add the rubys listed +damage to both min and max. It also does not include your hero's primary stat, any +damage bonuses or any attack speed bonuses from other items that you may have equipped.
Based on your images, the first one would be the best of the three. The listed DPS is slightly lower than the second, but has a higher primary stat and higher +% damage to elites, which are both not figured into the tooltip DPS.