I think ironically 40k is just as complicated with all the data sheets and FAQ’s and various books you have to reference
To be honest I would say both AoS and new 40K are as complicated as Warhammer Fantasy and proper 40K, but in an inferior way - where Warhammer Fantasy and proper 40K had complicated rulesets that took you all day to play but rewarded you with tactical complexity, AoS and new 40K have complicated and bureaucratic army list systems and pre-game admin that allegedly take longer for you to set up the game than to actually play it. I know which of those I'd rather have
It's been a long while since I played 40k (4th edition I believe), but switching from old school 40k to WHFB was a big upgrade in terms of tactical complexity. WHFB's limitations on movement requires much more planning and thought. Blunders in movement (and army deployment) are more heavily penalized in Warhammer Fantasy. Additionally, the fact that 40k typically leans more heavily on shooting, makes it an easier game to play. I haven't played any of the newer editions of 40k, but from what I've heard, I'd tend to agree with @Lord Agragax of Lunaxoatl . The scattered rules of AoS and the more recent editions of 40k, are not the type of complexity that a tactically-minded player yearns for.