I have both and I have them both drilled the same, 4 x 4 x 2. The biggest difference for me is the shape of the reaction. The Mutant is much longer and more angular in the backend, while the Invasion has a great mid-lane read and a stronger continuation through the pins. I actually stand a little more right (I'm a lefty) with my Mutant, but that depends on your oil conditions. Both need a lot of oil up front, they are the strongest pieces in my arsenal. But, I've found uses for both and I think they are different enough to own both of them. Hope this helps.
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