A kit lens is what you use until you put the lens you really like on the camera. The 18-135 is designed to be a walk around do anything lens, and it's probably the best at that. But it is strongest at about 24mm. That is well under the range of your 35 to 80.
So to me, the answer is pretty obvious. You don't shoot where the 18-135 is strong. Where you do shoot, 35 to 80, I'm guessing if you shoot a lot between 70 an 80mm, the 18-135 has already started to lose edge sharpness at that point. For the picture you posted, although the 18-135 will probably beat your 35-80 in terms of centre sharpness, but your subject fills the whole frame, the edge sharpness is important, and it's quite possible your 35-80 out performs the 18-135 edge to edge, at that focal length, and for that type of image. As well, portraits often look better softer. If you do a lot of portrait work, this could be the softness/sharpness compromise that suits your style. In all lenses, not just kit lenses, you have to be aware of their strengths and where you should use them and where you shouldn't. Obviously 35-80 is in your wheelhouse.
I have a Pentax 35-80, and even though it's not highly rated I love the images from it. But, 35 is not wide angle on APS-c, and I'd miss a ton of wide angle landscape images, if I carried it instead of the 18-135, and a lot of pseudo macro images. So most of the time it stays home. I just isn't the same lens on APS-c it was on 35mm film.
Sounds like for you, your 35-80 is a completely workable lens though. Enjoy.