I have both and quite some experience "tarping" in BC's mountains. I have an ID Mega Sola, which I prefer over the Wedge and I specifically purchased my Silwing, for an awning for this shelter.
The Silwing can, IMO, be pitched with a greater degree of tautness and it is big enough (barely) for this application. I also have the ID Poncho/St-I and it really is too small for doing this with any real protection from the elements.
I actually like my STIII for an awning over the two ID tents I have, one a MKI-XL and the other a MKI-Lite, bought from our good buddy here, "docdb". With these, one guy can rig a camp that will withstand any weather I have ever experienced and have a pretty fair degree of comfort.
So, all of this is to say that the choice here depends to some extent on the specific shelter one is using with the tarp and the "standard" ST-II, at 8x10', is never a "mistake".