Players are definitely not as limber and agile as in PES 2013.
If you want to check your Right Stick behavior, and if there is any lag, when not in possession of the ball (i.e. defending), hold the player select button (default LB) and move the right stick in various directions. You should see a line graphic on the pitch originating from the player currently being controlled, and moving in the direction you are pointing the right stick. As long as that is mirroring the movement you make with the right stick, all seems well on a technical level atleast.
As for right-stick dribbling, I find by far the best success in releasing the left stick, then holding the right stick in a direction I want to perform a feint, and then I wait until I actually want to perform the feint, at which point I will point the left stick in the direction I want the player to move after he does the feint.
Think of it as you "cocking" the feint mechanism by holding and not releasing the right stick, and when an opponent approaches and nears, you actually execute the feint, and move, by quickly also moving the left stick.
Works quite well, once you get used to the delay, and more skilled players have a pretty huge advantage over less-skilled players in how responsive they are and how quickly they can move the ball in certain situations. Some players are almost not worth trying skills with, they take longer to execute the feint than just moving normally.