Pros:

• Easy to put on and go: structure allows the shoulder to be positioned correctly, quickly, and without fuss.
  
• Pleats keep the fabric narrower at the rings, but spread pressure out evenly across your back, widening as much as you need behind the shoulder.
  
• Works on both left and right shoulders.
  
• Good for: most builds, from pointed to rounded shoulders.
  

Cons:

• Some wearers find pleats too structured, preferring to overlap fabric more or less than the pleats do.
  
• Can't be scrunched smaller (though wearing the rings higher reduces the amount the fabric spreads out)S.
  

Pros:

• Fewer, wider pleats makes the shoulder wider where it leaves the rings, and opens out faster than signature pleats.
  
• May be preferable for plus-sized wearers, as it fits a more rounded shoulder (this was my preference -- I have worn between an XL and 3XL in the last 16 years, and preferred a wider shoulder like this when my kids were babies).
  
• Works on both left and right shoulders.
  
• Also works for petite wearers who like to wear their rings high, as the wider spread allows a high ring while still providing generous support over the back.
  

Cons:

• Can be overwhelming on narrow or pointed shoulders, spreading too far down the upper arm, if rings are worn too low.
  
• As with signature pleats, can't be scrunched smaller.
  

Pros:

• Good compromise between pleated and gathered -- small pleats on both sides take up some of the width, partially restricting how far the fabric spreads out the fabric spreads over the upper arm.
  
• Once you find your "sweet spot", comfortable on most body types. 
  
• Gathered section allows the wearer to customize the width and amount that the shoulder spreads out.
  
• Works on both left and right shoulders.
  

Cons:

• Can take a little longer to put on than pleats -- if it's not arranged when putting it on, the gathered section allows the fabric to spread far down the upper arm, limiting range of motion and potentially causing discomfort.
  
• Decorative stitching isn't available with the Eesti shoulder, because the density of decorative stitches keeps the gathered portion from being scrunchable.
  

(I haven't tested my sewing with a gathered shoulder, so I'm not able to sew slings using a gathered style.)

Pros:

• Easy to sew, making it popular among sellers.
• Once you find the "sweet spot", comfortable on most body types. 
  
• Gathers allow the wearer to customize the width and amount that the fabric spreads out over the shoulder.
  
• Works on both left and right shoulders.
  

Cons:

• Takes longer to put on than more structured styles -- without careful arranging when putting it on, the fabric can spread far down the upper arm, limiting range of motion and potentially causing discomfort.
  
• If the fabric spreads too far down the arm, it's difficult to get the lower edge of the sling snug enough, leading to issues while wearing. This can be fixed with practice, but the learning curve is steeper.