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So, this is a weird question that crossed my mind about 8th ed. It looks to me that 40k and AoS have a lot of the same core mechanics, so could it be possible for 40k vs AoS games in the same way there are warmachine vs hordes games? come on guys, Tyranids vs Savage Orcs?
Possibly - if so I would use the 40k rules, and as sigmar units do not have S & T, work out what might be the likely stats for these (maybe compare strength verses a standard Space Marine e.g. a weapon wounds on 3+ therefore it could be Strength 5-7 aka wounding a marine on 3+, for toughness compare like for like - savage orcs = orks, sigmarines = primaris marines etc).
What Mr. Gold said.
That being said... Many of the minis seem to be interchangeable but I suspect that the grim dark future would win 9 of 10 battles against the grim dark past. Maybe 'Nids would be a fun invasion though?
However, there are Ork Snakebite tribes that shun modern technology (or perhaps it baffles them) and they could be drafted to armies the far future.
The two games are not compatible in the way you describe.