The Inquisitorial Stormtroopers being a distinct "thing" really started with the Eisenhorn novels (which features them several times), and then translated into them being a seperate troop choice when Codex Daemonhunters came out.
In neither case are they distinctly 'better' - the Inquisitorial Stormtroopers were quite clearly bad-ass in Malleus, but then so are the Kasrkin (one of them attacks a daemonhost with a combat knife, for heaven's sake!).
I think you'll find that a stormtrooper hanging round with an inquisitor in person will be better, but that's not meant to say that INQST>IGST, just that the Inquisitor went looking for a blunt instrument and found that guy (which is what Ascension stormtroopers represent). As noted in the Inquisitor quotes above, they may have better specialist training (this is a [insert random xenos species name]. Shoot here for maximum splattyness) or access to wierd and wonderful weapons (look, combi-stake crossbow!), but they're not necessarily better as general military troops.
It therefore depends on what you need. If there's a generic 'inquisitorial operation' the squad blunders into, then core rulebook stormtroopers are fine. If it's an inquisitor or interrogators personal retinue of half a dozen or so....they deserve to be specific characters, frankly, and the Ascension stormtrooper is more than justified.
Edited by Magnus Grendel, 12 February 2014 - 08:26 AM.