In your images, you'll see almost no difference between the 28-135 and 24-105 at the focal lengths and apertures they share.
It is nice having 24mm wide, but at the wide end the 24-105 tends to have more vignetting. On the other hand, a little more reach is often handy, but at the long end the 28-135 benefits from being be stopped down a bit to sharpen it up (f8, vs wide open at f5.6). If you look at resolution charts, the 24-105 is slightly better wide open, mostly in the corners. Both vignetting and corner sharpness will be seen more on a FF camera than a cropper. But the differences really aren't all that great.
You can see this at the above link, comparing the two lenses with the various tools on the website. Just keep in mind that those test shots are quite magnified, so you won't see as much difference in your images at normal viewing sizes.
The minimum focus distance/close focusing ability, USM auto focus performance, and IS effectiveness are all nearly identical. The 28-135 is 1/3 stop faster at 28mm. The 24-105 is 2/3 stop faster at 105mm.
The biggest difference between the two zooms is build quality and sealing. The 24-105 feels more solid and durable and it likely has better sealing against dust and moisture (neither lens is truly "weatherproof", though). Overall, the 28-135 is better than kit lens quality, is fairly typical Canon "mid-grade/USM" build quality.... It commonly has a slighly loose feeling front barrel, though that doesn't seem to effect image quality or focus accuracy at all. It's focus and zoom rings also aren't as nice as the L-series. The 24-105 feels more solid and "fine tuned", though it's not uncommon for it's red stripe to fall off. Both lenses tend to develop "zoom creep", where they self-extend while carrying them nose down. That's probably more common on the 28-135, but there are some cheap DIY fixes for it detailed online.
Of course, because so many have been sold in kit and some people react like a couple of the above posters, the 28-135 can pretty easily be found and bought very lightly used for around $200-250 U.S. New I think it's around $450, but I've never paid that for one. In comparison, the L-series lens costs $1150 new or around $750-775 used. Of course, the 24-105 includes a matching lens hood like most L-series, while the 28-135 the hood is sold separately for around $25 (tho all the used copies I've bought have incl. the hoods).
Over the years I've owned and used four or five different copies of the 28-135.... I currently have two of them I use on both FF and crop cameras as "walk-around" zooms, backups to my 24-70, and loaner lenses. Sometimes when I have to hike a distance with a big telephoto, I'll swap out both 24-70/2.8 and 70-200/2.8 for one of the 28-135s. That saves a lot of space and weigth. I've only briefly used the 24-105 and just couldn't justify 3X to 4.5X the cost for what is nearly the same lens, except for better build quality and sealing.
