As the title states, these 3 are the weapons I currently have.

The arguement here is going to be sustain vs damage. Are you living with the rare axe and echoing fury? If so, I'd probably stick with those.

If not, the life steal on the Won Khim Lau is likely going to keep you alive longer. I think you are really deciding between the echoing fury and the won kim lau though.

Looking at your profile I can see you are pretty well equipped. I think this is a no brainer. Keep the Mortal Menace as your main and use the EF on your off hand. The Won Khim Lau doesn't give you any IAS over EF and the bonus lightning damage still doesn't make up for the DPS of the EF. DPS trumps survivability in SC and having 2 weapons with LS is overkill unless you are doing mp10 runs.

Does it matter whether the EF or the rare is the MH, vice versa?

Pretty much, the only relevance for MH/Offhand is Barbs with their Passive weapon bonus. I've read, but haven't personally verified that Tornadoes only use MH for damage.

I have personally verified that DHs have 3 skills that only use main hand damage: Companion, Fan of Knives (wtf?) and Rain of Vengeance. Even Sentry and Trail of freaking Cinders use the weapon that will be swung next for damage calculation.

As far as Monk skills go, I only know that Sweeping Wind uses combined dps, but I would guess pretty much every other relevant skill is only based on which weapon is going to be swung next. You can quickly check this on your own by equipping your normal MH weapon and a ilvl 5 axe in your offhand. You'll very quickly discover which skills use which weapon. Just remember that skills which don't actively swing the weapon won't necessarily alternate. For instance, Wave of Light may stay with your MH weapon damage until you actually attack with it at which point Wave of Light will only use the OH weapon (until you attack with your OH and then Wave of Light would only use MH).

Check it out on D3up to see what's best. I think Yoyo is right and that you should use you axe as a main hand. But whether or not you should use your Echoing Fury or Won Khim Lau, I'm not sure and should be input into D3up to be sure. I have a feeling that the Won Khim Lau will actually be better. Sheet DPS will tank for sure though.

After simulating it on D3up, and checking out the skills damage tab, it turns out WKL does a little more damage on SW, but the EF does overall a better damage on my main attacks and I have 1+ spirit generated per second.

Good topic as my HC monk Plvls as TR, but for ubers I plan to be SnB or dual wielding.

So running the numbers how do you choose a weapon?

Overall dps drops without EF but how much of a drop is allowed type thing?

I had consider MH wlk and OH EF to be the cats meow.