The L primes will give better IQ than most all zooms. (keep in mind resolution isn't the only thing that contributes to IQ)
Even the 24-70mm II will only match or slightly beat the L primes in resolution. It is still behind in other areas.
But that is not the difference you are feeling with your shots.
To use an painting comparison the primes give you a larger pallet and higher quality brushes to work with.
You not only have the improved IQ of the prime but the prime is able to use wider apertures.
The same is true of using a FF over a Crop camera. The FF will give you more creative potential.
So for me yes the Primes "take better pics" because I utilize the extra tools they provide.
I'll name a few of the (good) 'prime' advantages aside from resolution: Color rendition, contrast, flare resistance, less distortion, possibly better bokeh etc. Primes also handle differently, generally they're lighter and easier to handle (no zooming) so less to distract from photography.
Well of course though, the 24-70L II handles those better than the primes in that range, including the 35L and 50L, at f/2.8. So the 24-70L II is an exception. It's better. The only disadvantage is that it can't go wider. I sold my 35L and 50L once I got the 24-70L II, because the IQ, including everything, was better and yes I noticed it in my photos.