Room Treatment

IME, Acoustic panels are primarily designed to absorb sound waves to reduce room echoes and reverberation, while acoustic diffusers scatter sound waves to create a more balanced and natural-sounding acoustic environment. Check out some of the very best rooms in Audiogon Virtual systems to have better understanding and placement of these two very critical but different acoustic treatments. 

@lalitk It's hard to get clear on this for a lot of folks. If you go to Acoustimac's website, it aligns "acoustic panel" with absorption. If you go to GIK, the first things displayed are diffusers but they also have absorption on the page.

Viz. https://www.gikacoustics.com/product-category/acoustic-panels/

I see GIK and other sites like it have panels for absorption, and Decware has diffusers which look like window slats or turning vanes, and they recommend one for each wall. I was looking to see if anyone has experience with both, and what application works best for a standard 15x15 listening room with gypsum wallboard walls.

A "panel" is a generic term. 

Panels can be absorbers, diffusors or a combination.  There are also bass traps which are a type of absorber that is especially effective in the bass region. 

GIK makes some panels which are a combination with absorption materials behind a diffusion grid.  This allows for high frequency diffusion along wiht mid range absorption.

“what application works best for a standard 15x15 listening room with gypsum wallboard walls.”

I recommend you seek consultation from GIK, they provide free consultation. Whatever they recommend, I suggest you treat each area in steps. This will allow you to understand the impact of acoustic panels/diffusors and further evaluate the need to treat your room. It’s easy to overdo absorption and kill the liveliness of a space, especially in a smaller room; hence my recommendation for doing it in steps. Not knowing your room, we are just shooting in dark here. Let’s say you have a conventional room with four walls + ceiling which gives you five areas to address,

Front, Back, Sides, Ceiling and Corners.

Starting with the first reflection points (side walls and ceiling) usually gives the biggest improvement in clarity, while bass traps in corners help smooth out low-frequency response. The back wall can be tricky—some rooms benefit from absorption, while others need diffusion to maintain spaciousness.

Hope this helps!