First step in the research is to check out the owner's manual to compare the features. In the first place, I don't think the Yamaha line has either USB or FireWire connectivity. So if you are planning to use the mixer for computer-based recording, you would still need to purchase some sort of interface. Although I have no experience with the USB or FireWire units in the MultiMix line, I understand the basic thinking at Alesis was to create a mixer which could be used conventionally or as a digital interface. And even though I have issues with Alesis over their customer service [or more pointedly--the lack of consistently good customer service], I think in this area they are to be commended for at least making an effort to provide working musicians on a tight budget with some tools that are capable of multitasking.
In addition, I checked the Yamaha MG__/__FX series out via the owner's manuals before I bought my Alesis MultiMix6FX. The Yamaha's FX are limited to a like 16 settings of varying types of reverbs and delays. Again, I don't know if the FX in the USB and FireWire versions of the Alesis line are the same as the "regular" MultiMix line, but the FX in the regular line include, in addition to reverb and delay settings, chorusing, flanging, pitch shifting and some combo FX. Granted, for the price, they aren't state-of-the-art, but they aren't bad as long as you are satisfied with that limitation. It's basically like purchasing a Mixer with a built-in NanoVerb unit. I added a SmashUp and a Faze unit from the ModFX line to the signal chain and I'm pleased with the results.
After you've checked everything out on paper, the next step is to determine whether or not you have any local dealers who will let you "test drive" the units. Then see if they will match, beat, or at least come in the ball park of what the warehouse dealers charge.
Keep us posted on how your search goes.
