Originally it was hold RT to run hold RT and A to climb. AC III got rid of the hold A part. It didn't really change much (I still held A out of instinct anyway) but it cut down on the amount of times the character would just leap off to his death.
I really like the current system where you still hold RT to climb but now hitting A has you climb up and B has you climb down.
There was a certain rhythm to freerunning in pre-AC III games. It was just basic input and it wasn't anything to master, but having to time jumps, grab ledges, weave through the crowd or do leapgrabs was something to break the monotony of just pushing a button and tilting the analog stick and letting the game do everything for you.
III and then Unity made movement more responsive, but also removed that basic level of player interaction. The drastic reduction of climbing puzzles only exacerbated that. You don't really need to maintain even just that basic awareness while running or pay attention to the structure of the building you're climbing on.
And now Origins is taking it to the next level by emulating Breath of the Wild. Fine, traversal will be faster, more seamless. No more obstructions. I grew tolerant of III's changes over the years and freerunning in these games is still fun after all. Especially Unity's revamped movement gave a tremendous feeling of gracious elegance, speed and control while bolting across the rooftops. But it wasn't always like this, the PoP roots of the series used to be quite noticeable in the first couple of games.