My experience:
Nano 6: 1.5 years of use, very flexible shoe, not as stiff for weightlifting as the Nano 8 but better versatility. Is better for running but not as goos as a dedicated shoe.
Nano 8: ~7 months of use, more stiff than the 6, more sturdy also and the sole is more firm, so is better for wl; is also more comfy but for running the 6 is better.
Adipower: got them ~10 months ago but barely touch them; they are weighlifting focused, an specialist tool, with a extremely sturdy and firm sole, but useless for everything outside snatches, cleans and squats. They are excellent for the task, but with a narrow sole and ultra stiff heel, shouldn't be used outside static liftings.
I also have a running Adidas shoe (don't known the reference) which endured well the last two years (good for running but not for lifting: the heel is too soft and shrinks under heavy lifts. My only advise about running shoes would be to not go for the ones with a foam cushion because they wear off very fast (I'm not an specialist, maybe that is what they should do, but a shoe that wears off in 4-5 moths seems to me a bad trade if I can get a metcon hybrid one which last a year and half...).