All PRS singlecuts have wide-fat and not wide-thin necks unless they are one-offs.
The price of a bare bones Singlecut (no birds, no gold h/w, no 10 tops) is $3.5k -$3.8k (I can't remember which one it is since I asked a couple of years ago)
That whopping $6k Singlecut at Davis is the 20th Anniversary package series which has an artist top (better than 10 tops), gold hardware, 20th Anniversary birds and a brazilian rosewood fretboard. A tricked out Singlecut.
You will be paying in excess of $6k in US dollars for a Gibson Custom Shop Historic R9 Series with a brazilian rosewood fretboard. And QC would still not be up to par as compared to PRS, yes even for the custom shop models.
Tonewise, the singlecut sacrifices that low-end thump of a les paul (or muddiness otherwise 8) ) for brightness, clarity and definition. The mahogany-maple ratio of a singlecut (less mahogany, more maple) is different from that of a les paul.
Basically the Singlecut will sound more aggressive and more balanced than the les paul. That said, nothing beats a les paul for its characteristic low-end thickness in tone and warmth.