I am looking to purchase a mixer and am keen to know the practical difference between these two mixers. The price is about the same.
What circumstances would you prefer the one over the other?
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Dr. Mayhem was right about the straight forward differences between the 2 models. However I'd like to refer to the "Under which circumstances would you prefer the one over the other?". So usually, you won't be using the Graphic EQ while utilizing the mixer for studio tasks. In studio you will be more interested in preamp and whole channels quality, maybe even disregarding the channel EQ while preferring more quality software ones (at least in not very expensive mixers). However graphic EQ will be more usable for "field" tasks (PA) where you might want to correct the overall sound to fit the acoustic properties of the location. So just to summarize, the one with graphic EQ seem to be more targeted on PA jobs and the second one on studio work.
P.S. I'm a bit puzzled by the fact that the very standard set of solo, mute and the signal routing buttons are absent. I would expect them to present on the EQ model mixer particularly.
The two pages you have linked to describe the differences very well. If you read them you will see that the key differences are that the 1222 has a 7 band graphic eq, feedback detection system, surround sound effect and a voice cancellation function, that the other model does not have.