The next question is which selection tool should one use first. The choices are:
a) an initial selection with (say) the quick-select tool followed by a 1st refinement using Refine Edges, followed by a 2nd, lighter pass, again using RE;
b) Topaz's ReMask, followed by a 2nd, lighter pass with RE;
c) OnOne's Mask Pro, followed by a 2nd, lighter pass with RE;
d) Vertus' Fluid Mask, followed by a 2nd, lighter pass with RE;
e) Some classical method such as using channels, followed by a 2nd, lighter pass with RE.
I never use Method (a). If one pass with RE doesn't cut it, a 2nd pass with RE doesn't help very much.
I haven't used the "channels" method, ie, (e), in years. All of the 3rd party plugins work by performing a vastly more sophisticated version of the channels technique and I find absolutely no reason to go back to it.
In the conventional "channels" masking technique, you look for the channel with the best contrast between subject and background. In contrast, all three of the plugins listed above look locally for the best differentiation between the subject and the background using both hue, saturation and brightness. So, if on one side of a subject's head, the background is a dark blue sky, whereas on the other side, the background is very bright warm colors from a sunset, all three of the commercial plugins will adapt (or can be made to adapt) to accurately find the edges on both sides of the head, whereas a situation like this will completely throw a simple "channels" technique.
The ultimate extrapolation of the above situation is an image where both the background and subject have variegated / patchy colors (eg, whispy hair against fall foliage with patches of sky peeking through gaps in the leaves). This will stress any of the algorithms / plugins, but with familiarity and good technique, one always gets the best result from one of the commercial plugins followed by a final tweak in Refine Edges.
With respect to choosing one of the three commercial plugins, I would recommend Topaz's ReMask. It's the simplest to use, and the results (with proper technique) are as good as either of the others. IMHO, OnOne's Mask Pro is a bit more difficult to use, whereas Vertus' Fluid Mask probably can be tweaked to produce astonishing results, but there's a lot of things to learn how to tweak.
HTH,
Tom M