I just went through this myself. I did print the same image using QTR using Epson K3V inks, and the ABW mode. The ABW did look sharper, and initially I kind of liked it. But when I looked at it more closely, I started to hate it. Here's why.
I did have ABW, QTR, and also piezography prints made up. When I compared the ABW and QTR versions, I found out how ABW was achieving the sharpness. First, by crunching the shadows into blacks, the dark greys became either very dark, or very light. Along edges, this had a sharpening effect. Any detail that relies on a transition from dark to light grey will be altered or lost completely. You are also not in control of sharpening. If you have your image sharpened just as you like it, ABW will sharpen it more. If you like that, than ABW is for you. If you want to be in control, QTR (or piezography if you want to go further) is for you.
The three prints I had made up (actually 10 in total, 5 on matte, 5 on glossy) adjusted to keep the overall tonality as similar as possible. The QTR and piezography prints came out fairly closely matched. The fellow who made the prints has a profile that compensates for the crunching of the deep shadows which actually did produce edges similar to both QTR and piezography. However, the prints using QTR or ABW were very sensititve to lighting conditions. When I compared them to the piezography K6 print (which uses 6 shades of grey and no colour ink), the QTR-K3 print looked warmer than the piezography print under warm lighting (halogen desk lamp), but it looked cooler than the piezography print under cooler lighting (LED room light). When comparing the ABW and QTR-K3 prints, they looked almost identical under warm lighting (ABW had slightly warmer shadows), but the ABW looked significantly cooler than the QTR-K3 under the cooler lighting. When viewing them under a loupe, the ABW uses the most colour inks in the black and white, presumabely to tone and neutralize the blacks. QTR uses less colour ink, but it's still there. Piezography uses no colour ink because all ink positions are grey or GO. ABW seems to be the most sensitive to lighting conditions and will its change appearance under warm or cool lighting. QTR is more forgiving of lighting conditions, but the effect is still there. I am convinced that the colour inks added, probably the cyan, reflect a significant amount of blue light from cooler light sources such as LED lighting. Because there are no cyans in piezography (shades of grey), the excessive blue light in cooler sources is not reflected the same way, except perhaps from the paper itself. (Although, piezography tends to cover even the highlights with the lightest shade 7 for K7, or 6 for K6, which would further reduce the amount of blue light being reflected from LED sources.
All of this representss qualitative observations, so it's not really scientific. I could try measuring it with a device and prove my points, but I'm convinced for myself and I have other things to do other than prove this one experiment. Besides, I don't have a measuring device yet.
As David said, one should probably print the QTR and ABW yourselves to see. I thought I'd include my own observations though.
Larry