For mainstream audiences, there is a general sense of apathy for a bland Spidey film. But if you go to fan communities (like on this site), it is like a feeding frenzy of hate for the Raimi films.
As for Batman, I would not mind the Arkham visual style being embraced to a degree (though I hope no actress has to wear those outfits designed in those games!), but I honestly think Nolan took who I always thought were the five best Bat-villains (Joker, Ra's, Two-Face, Catwoman and Bane in that order) and crafted a great trilogy around them that both was heavily influenced by iconic Batman stories (Year One, Long Halloween, Dark Victory, Knightfall, No Man's Land, etc) and equally took influences from our culture and society during the turbulent years the films were produced in.
I like that approach a lot. The only major villain I felt like they missed was Harley Quinn. So, if the new trilogy is forced to do what Webb did at least with the origin, which is arbitrarily the opposite of what came before, while the tone may be great, narratively there will be problems.