Photoshops Shadow/Highlight has more controls than Nikon Capture's Digital DEE (but the latter uses extra information recorded by the camera). Also Shadow/Highlight can produce some unnatural effects (sometimes interesting).

Which should I use as my first port of call when adjusting shadow detail?

Both are pretty powerful tools. As stand alone, I would have to say that I generally prefer to use highlights/shadows. Even with more options it seems more intuitive and certainly faster. However, in conjunction with the Unsharp Mask functions in Capture, DEE can certainly give different and very powerful results. At the same time, working as long as you can in RAW has got to reduce manipulation deterioration. (yipes! Did I actually say that?)

Cheers
Dave