The difference in technical quality between the two sample images is striking! Particularly the difference with regard to chromatic aberration. How much of the rest of it is attributable to the different lenses, however, is debatable. If you were shooting handheld, the differences in "sharpness" could be due to more camera motion in one shot than the other.

The problem is that too many new photographers think that buying a new lens with measurably better technical performance¹ will also improve their shooting technique, compositional vision, and lighting skills. It won't. At all.²

It just means they'll get sharper images with less chromatic aberration of the same poorly composed, badly lit, boring photos they were taking before.

If they are shooting handheld using less than stellar technique, the non-stabilized EF 24-70mm f/2.8 L II could actually give them blurrier photos than the EF-S 18-135mm f/3.5-5.6 IS.

Shooting handheld at 1/60, this is apparently what happened here. The IS of the cheaper lens prevented mild camera movement from blurring the photo. or maybe the camera didn't move at all when the cheaper lens was used. The sharper lens without IS is blurry because camera movement that occurred during that shot was not counteracted. It's not because the lens is less sharp. When you zoom in to a piece of an image that is 1/10 the width of the full image shot with a 24mm lens, it's the same as if you'd used a 240mm lens in terms of blur per image width for a specific amount of camera movement. The 1/FL*CF (focal length x crop factor) rule of thumb says shooting hand held on a crop body at 240mm magnification without IS one should use an exposure time of 1/400 or shorter if the full image is to be viewed at 8x10 or 8x12 inches. Your exposure time is over 6X longer than the recommended Tv.

I'll make a sort of confession. I have an original EF 24-70mm f/2.8 L. It's nowhere near as sharp as the EF 24-70mm f/2.8 L II. In fact, it is not even as sharp as the Tamron SP 24-70mm f/2.8 Di VC. It is sharper than the EF 24-105mm f/4 L IS when both are on a very stable mount. I rarely use the 24-70/2.8 instead of the 24-105/4 IS unless the camera is going to be on a tripod. Why? It's a sharper lens with a wider maximum aperture. Why would I possibly choose the less sharp f/4 lens, even when shooting in low light? Because as I age my ability to hold the camera perfectly still is not what it once was. I'm still pretty good, and can still do better than most novices one-third my age. But I'm not as good as I once was. And I'm not as good as I need to be to shoot at 70mm and 1/30 or 1/15 second at f/2.8 with an unstabilized lens versus shooting at 70mm and 1/15 or 1/8 second at f/4 with a stabilized lens. If the subjects are moving in that kind of light, it's way past time to get out the fast primes and put the zooms away.

A better lens will usually give better acutance and less aberrations. But a better lens won't somehow magically cause the light to be transformed or the colors to balance themselves better and "pop" off the screen/page. That's the job of the photographer, not the lens.

¹ Technical performance of lenses measured in a lab is normally done with the camera mounted on a very sturdy tripod, the lens precisely focused manually, and the shutter released remotely. Often, mirror lockup is also used, even though excellent lighting, including very short duration flash, is used to allow shorter exposure times.

² IS/IBIS can make up, to one degree or another, for poor camera stabilization technique. But it does not actually improve the photographer's technique, it only hides, to one degree or another, the photographer's lack of better technique.