Vanquish is a far better shooter at encouraging movement, primarily due to the fact that you can still move freely on higher difficulties. With Uncharted, your ability to move freely is crippled on higher difficulties, like Crushing. You die very, very quickly the second you pop your head out of cover. However, on easier difficulties, you lose motivation to move from cover to cover as there is no longer any real reason to move. Enemy damage becomes a joke and you lose all urgency. With Vanquish, boost allows you to move quickly around the arena and avoid damage.
I imagine that the sprint function in Uncharted 3 was introduced as a way to move quickly from cover to cover on harder difficulties. However, they gave enemies the sprint function as well and had really screwed up enemy placement which negated all of that.
With Uncharted 4, ND has introduced the different alert states for enemy encounters, like The Last of Us, which will definitely encourage mobility. You can move freely around the arena as soon as the enemy loses track of you. This is something that would still apply on harder difficulties, which should allow you to be very mobile, even when enemies can two or three shot you.