I dont have a 28-105 to compare them to.
The 28/2.8 gets poo-poo'd as being a low end lens, and from the mechanical standpoint, it is. No USM, cheaper (and lighter!!) construction. However, its imaging qualities are not too bad, especially considering its cost. Fairly contrasty, quite acceptable quality of imaging at medium lens openings. There is some falloff in brightness at the edges wide open, and as we know, digital magnifies the vignetting effect. Stopped down, even a little, its quite nice, and has less falloff than the 18-55 at its comparable (28mm) setting. The focus is fast despite lack of USM because not much needs to be moved to make it focus.
The 28/1.8 is much more robustly made. It accepts a petal type hood. It has internal baffles to help against any flair from being formed. Wide open, not bad, stopped down even 2/3 stop, and its very very nice. The 2.8 is not noisy, but the 1.8 is absolutely silent in its focus. Vignetting is minimum on a 1.6x crop, even wide open (just a little, but it gets better when stopped down just a little bit).
Both lenses are free enough of barrel distortion as to qualify as totally acceptable, except for critical technical use Both are relatively flare free. Neither has bad chromatic aberration issues, but the 1.8 is more highly corrected.
My opinion still stands - if you need the speed and extra little bit of IQ, the 1.8 is better. If you're more interested in having a small, very light 28, then the 2.8 is better. I tend to grab the 28/1.8 more often than not.
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Livin' the blues, one note at a time