I can sum it all up in one simple idea. Pokemon in ADV were usually problems you had to account for. Pokemon in DP are opportunities. In ADV, there was a big sense of having to account for all the threats and you felt really stretched when building teams. In DP, for now at least, thinking like that doesn't really work out. It's easier to make an independent threat so you stop thinking "how do I get past Blissey" and more thinking "how can I exploit Blissey?". Even powerhouses like Garchomp work this way. Thinking of walling Garchomp only goes so far; you mostly have to think of what positive things you can accomplish because your opponent sent out a Garchop. I find this shift makes the game WAY more fun and allows for far greater creativity. I can tell a lot of people don't "get it" and whine constantly about Pokemon like Blissey and Cresselia when, in fact, these Pokemon are just golden opportunities they are failing to exploit.
I don't think it's all in the mindset etiher. In ADV, you can't look at a Tyranitar with a sub up and think "opportunity". No, there's no way around the fact that it's nothing but a problem. It's not like you can set up on ttar in DP either, but you can much more plausibly just predict resist switches to get in something fast that can kill him fast. He runs Ice Beam to kill things like Hippo that stop him dead otherwise, but that's a perfect switch-in for both Infernape and Weavile! You can really do this sort of thing so much more in DP; it's really the better game.
I don't think it's all in the mindset etiher. In ADV, you can't look at a Tyranitar with a sub up and think "opportunity". No, there's no way around the fact that it's nothing but a problem. It's not like you can set up on ttar in DP either, but you can much more plausibly just predict resist switches to get in something fast that can kill him fast. He runs Ice Beam to kill things like Hippo that stop him dead otherwise, but that's a perfect switch-in for both Infernape and Weavile! You can really do this sort of thing so much more in DP; it's really the better game.