The question is pretty straight-forward: a monk can hold a single weapon (with or without a shield), two weapons or one of a certain subset of the two-handed weapons. Is it ever possible for a monk with a two-handed weapon to do as much damage as an optimized dual-wielding monk?
Overall DPS is a hard thing to qualify without a lot of number crunching however the logic behind the two different systems you mentioned are this:
I can only assume Blizzard balanced this out so over time (say, a minute?) they are somewhat equal.
An example of my build: I use Fire Ally, Seven Sided Strike (+Ult AoE Rune), Serenity (+Heal Rune), Lashing Tail Kick (+360 Degree Rune), Evasion Mantra.
The ally is doing 40% of my weapon damage and 7SS is doing 777% (plus the explosions) the damage on these two would be much lower with dw although I would have more spirit to spend, but considering the build I use; I have two substantially long lasting spells, one with a huge cool down and two with low costs. 2h is a no brainer for me.
However if you wanted to use wave of light for example with it's huge cost of 75 spirit dw would be the way.