Q:

AABB Collision Detection Confusion

I am trying to understand and implement AABB collision to learn simple 2D game physics.  I'm following a tutorial and its method is a bit different to other websites.  It uses the center of the object and its "half-size" to determine collision.  This is its code:
public bool Overlaps(AABB other)
{
    if ( Mathf. Abs(center.x - other.center.x) > halfSize.x + other.halfSize.x ) return false;
    if ( Mathf. Abs(center.y - other.center.y) > halfSize.y + other.halfSize.y ) return false;
    return true;
}

And this is the seemingly more popular option:
if (rect1.x < rect2.x + rect2.width &&
   rect1.x + rect1.width > rect2.x &&
   rect1.y < rect2.y + rect2.height &&
   rect1.y + rect1.height > rect2.y) {
    // collision detected! 
}

Which one is more efficient?  And for the first option, would I define the center and half-size like this:
AABB = new AABB(new Vector2(Width / 2, Height / 2), new Vector2(Width / 2, Height / 2));

Center and half-size method source: https://gamedevelopment.tutsplus.com/tutorials/basic-2d-platformer-physics-part-1--cms-25799
Position and width/height source: https://developer.mozilla.org/en-US/docs/Games/Techniques/2D_collision_detection

A:

Efficiency of both depends on how do you use AABBs. 
Center/half-size pros:

Easy and fast retrieval of AABB's position
Collision detection may be easier to understand
Easier to understand calculation of AABB's border position

Center/half-size cons:

Each collision detection will have more operations (subtraction/addition)
Multiplication when retrieving AABB's size

Position/size pros:

Collision detection has less operations (which doesn't necessarily mean it will be faster, probably not much unless you do millions of them during single frame)

Position/size cons:

Heavier calculation of AABB's center (division by 2, so nothing scary though). 

If you often need to update/retrieve AABB's center position, first option might be faster.  If not, second one. 
Best way would be to implement both and profile the application, or just use the one is easier for you to understand and use.