Whilst I agree somewhat the biggest difference I've seen in their style of play(for both Spain and Barcelona) is winning the ball back.
A few years ago even if you managed to get the ball off Spain/barca they would be all over you and you'd barely have time to get your head up, the ball very rarely got out of the oppositions half of the pitch.
The past couple of years there's been nowhere near that intensity of pressing, and so the defence actually gets exposed and has to do some actual defending instead of just mopping up and being available for a pass, and it turns out they're not very good at it.