Bookshelf vs diffuser panel. Who wins?

Well. They are kind of the same. The real question is how much diffusion is best for your speakers. These are floor to ceiling bookshelves? You can pull books out an inch or so randomly changing the book surfaces to be highly irregular. 
 

Different speakers require different ampunt of diffusion. You can experiment by throwing heavy blankets over the bookshelves. See my systems. A thick wool oriental carpet has really improved my system. Pillows across the bottom killed the fan noise from my amp and low reflections. 

Where is that bookshelf located vis-à-vis your audio system? A bookshelf is definitely better than nothing, but it cannot possibly compare with a properly designed diffuser panel. I used such bookshelves to mimic diffusers early on, but once I tried diffuser panels (GIK Alpha 4a), there was not going back. The 4” Alphas are combination absorber, bass trap, and diffuser. I now have 14 Alpha 4” and 6”.

Here is copy / paste from GIK website:

The key to good diffusion is an even scattering. A quality diffuser should scatter the sound in a complete 180 degrees. GIK treatments like the gotham and alpha series are designed with a mathematical formula to give a perfectly even scattering.

Good diffusion doesn’t happen by accident, the designs are very precise and complex. Some people suggest using a bookcase filled with books as a cheap form of diffusion, but a random assortment of books is extremely unlikely to have the layout precision required to produce good diffusion. It’s probably better than a bare, reflective wall, but it won’t perform like a good diffuser.

full and healthy bookshelves perform a similar function to room treatment and (more importantly, imo) makes a space cozier and more comfortable to be in.

i have nothing against professionally treated rooms - they sound amazing - but i personally prefer a comfortable space surrounded by the things that i love and value to some sterile, professionally treated, Serious Listening lair with a single chair and 50k in electronics on the floor surrounding the obelisks from 2001: a space odyssey. i could hit the lottery tomorrow and would still gladly make that sacrifice (or alleged sacrifice) in sound quality 8 days out of the week 😂

Personally I can't stand bookshelves in rooms. You have to fill them with books or assorted pictures and objects so they will hopefully interest visitors. U are Stuck with them.

Much prefer the blank canvas of a wall that you can decorate much more creatively.

What wins?  Artificial ficus trees win.  Get a few 5' - 6' artificial ficus trees and use them as diffusers.  Much more effective than bookshelves or wasting money or time on diffuser panels.  I have over a dozen in my listening room and they are great.  And have a VERY HIGH Wife Acceptance Factor value.