Rob, there are several members, including myself, who have spent considerable time with both the 404 and Omega II. I own both and would be happy to do some comparisons using the 007t amp if you are looking for something in particular for your musical tastes.
For most music (I listen to all sorts of stuff), I prefer the Omega II's because of their honest, even-handed presentation of music throughout the frequency spectrum. The Omega II's tend to get out of the way, leaving nothing but the music itself (i.e., nothing is overemphasized). If anything, they give some emphasis (but not overemphasis) to the lower regions, but their bass is clean and focused and not at all overextended. The Omega II's bass is, dare I say, "musical" in the sense that you really appreciate the weight and texture of Charlie Haden's upright bass, or the cannon blasts in the 1812 Overature. You're on the battlefield!
For certain selected music, I prefer the aggressive nature of the 404's (i.e., Van Morrison) because they get your foot tapping with their forwardness. Yet, the 404's are quite colored and arguably bright (similar to the RS-1's in their emphasis). If you're a rocker, they might just be your perfect everyday headphone. When I first heard the 404's at the Florida head-fi meet in December, my immediate reaction was "Wow! These things are ALIVE!" No doubt about it, the 404's put you in the front seat, and there is nothing wrong with that! IMO, the 404's signature is quite nice at times, but not my first choice for everyday listening.
Keep in mind that the differences between the 404's and Omega II's are not at all subtle. Although the famous Stax 'transparency' is present in both, they are in some ways almost polar opposites of each other. One of my friends said, "I cant' believe these two headphones are manufactured by the same company! Are you sure?!?!?" There is even a volume difference. When going from the 404's to the Omega II's (on the fly while driving both with the 007t), you need to turn the volume up from 3 to 4. Or, more to the point, when you put the 404's on, you need to turn the volume down because of their forwardness!
Independent of each other, I like both of these cans a lot. If I were to listen to the 404's for a couple of hours and then put on the Omega II's, I'd be bored at first. Everything becomes overly subdued -- at first -- and, by comparison, dull. But then after a hour with the Omega II's, you can't yank them off of my head, and to put the 404's back on would be the functional equivalent of jumping into a cold shower when you first get out of bed. It would be too much of a shock once you're settled into the Omega II's warm embrace.
(Check with ServingInEcuador and Matt who have both done comparisons using KGSS amps. Yes, 'Matt' is his username. Also, immtbiker did some comparisons at my place with the 007t.)