No opinion here - it looks like you processed the pic in ACR and PN with different goals in mind. The PN pic looks like having "excessive" contrast and saturation, something you also can achieve with ACR.
It is only recently that I became aware that I was mistaking software presets for software "signature". Presets are quite arbitrary and relate, probably, with marketing thoughts, a bit like the warmish-yellowish cast imposed on printed photos by the shop around the corner - shouldn't all those summer snapshots be filled with sunshine ?
I am pretty sure that, as long as you stay far from extremes, you will be able to produce similar results with both pieces of software. I'd expect biggest differences coming from highlight recovery, shadow recovery, sharpening, and noise reduction (especially in conjunction: de-noising + sharpening). Your sample picture does not however test any of these *probably* discriminating factors.
The Fierce Bear of the North mentioned highlight recovery as one strength of PN. I'd be curious about the other criteria. I have not tested these for myself yet. In my D700 times, I was more interested in de-noising, and at the time, DxO was the clear leader. Meanwhile, sensors have improved (D800, Df...) and I do not care much about the remaining differences between DxO, ACR and RawTherapee. Right now I am more concerned by proper rendering of reds, as I am shooting lots of small flowers and not seeing any details in their oversaturated petals. Here the problem seems to be 1) an intrinsic weakness of Bayer matrix sensors (foveons seem better); 2) a software default setting issue (the "Adobe standard" profile sucks).