Types of Bags

Sling Bags

Pros

Enable a very fast transition from rear to front of body with minimal use of fine motor skills.
Transition of bag from rear to front naturally provides greater coverage of the user’s core, which better supports use of a ballistic protection insert.
The strap sitting diagonally close to the center of the bag means it is generally tighter against the body in both rear and front positions. This provides the user a more stable platform for drawing the primary weapon or retrieving contents from internal pockets, such as spare magazines.
The stability of the bag provides the user greater freedom of movement, including running, crouching, etc.

Cons

The bullet-shaped sling bags tend to have a narrower depth of compartment, making storage of the PDW equipped with a full-sized magazine a challenge. This limitation can be mitigated by storing the PDW with a shorter magazine in the weapon and having full-sized magazines ready in pouches for reload.
Triangular-shaped sling bags are somewhat unusual shape, making them a less discreet option than a bullet-shaped bag.

Messenger Bags

Pros

Depth of compartment may better support storage of PDWs with longer magazines.
May have built-in features that support quick conversion to a chest rig (i.e. a waist strap to keep the bag snug against the body, a shoulder strap that can be rapidly shortened to make the bag ride higher on the body, etc.)

Cons

The strap being connected to the bag at the top two corners makes the bottom prone to movement. If bag supports conversion to a chest rig, this can be mitigated by use of the waist strap
The bag may have a top flap the user must pull back to access the main compartment, which may slow the user when attempting to draw the PDW.