I have not used the 28-135, but many years ago I used the 35-135 USM with a film camera and found both handling and IQ to be excellent. However I did use the 28-105 f/3.5-4.5 USM with DLSRs for a long time, and liked it a lot. There is not much wrong with the IQ delivered by the 28-105 f/3.5-4.5, even in the corners, as you can see in this un-cropped, full frame shot (with the 16.7Mp EOS 1Ds mark ii):
... and unless you are shooting fast-moving subjects in poor light the apertures are plenty fast enough.
Someone above suggested looking at the highly praised 24-70 f/4. I recently bought that lens for the wider 24mm angle, for the genuine Macro capability, but most of all for the Image stabilisation.
It is a lovely lens, and lets me get images in low light that the 28-105 would not.
I do not miss the focal lengths from 70-105 (and if I want them I can user a different lens) and although it is noticeably heavier that is not a problem, but the extra bulk makes it less pleasant to handle than the old 28-105. As for IQ, there might be marginally less distortion, and slightly more detail and sharpness, but the tiny improvement would not justify the "upgrade". The change is justified only if you "need" (i.e. want!) the weather sealing, the 24mm FL, IS, or a decent macro (without having to carry a specialist lens like the 100 f/2.8 macro)