Experiencing the same with the difficulty in online play, solo battles, and challenges. Using the same roster/players but changing the difficulty results not only playing a harder, more efficient team (I'm okay with that) but my team's players are dramatically dumbed down and slower. The difference is very unbalanced and inconsistent. It's like it's not just based on better AI play, but skill sliders (increase the CPU skills, decrease YOUR skills) which makes it almost impossible to call run plays because of how slow running backs react off the snap.
As the OP has mentioned what is the point of players stats? Player attributes and the play experience with them should be consistent throughout all playing difficulties. i.e playing speed should be the same in All-Madden as it is in Rookie. Currently it feels like our players are being slowed down. Unless it's just because the CPU is now sooooooo much faster, that it just "feels and looks" like we are slower. Either way it seems like there is a pretty large gap between Pro, All-Pro, and All-Madden that could be tweaked to make the experience a bit more competitive.