As an Arsenal fan, I would rather José get the job than Giggs. Sure, you might win a trophy or two in his years at the club but it would be hilarious to watch as I'm certain José at United will end in tears and that much is self-evident.. it's too combustible a situation not to. A demanding fanbase, a coach who respects nobody but himself and prefers to make himself feel more important than the club.
It would be a poor move for United in the long-term and one which could see the name of a great club dragged through the mud at the expense of José's ego. It's okay for a smaller club like Chelsea to accept this fate... but for United it would seem a little desperate.
As for Giggs, it would be a poor move in the short-term (potentially) but a good move in the long-term. One thing, as an Arsenal fan, that I do not want is a Man United man leading Man United through these more challenging times for your club. I want you to continue to employ poorly with managers who are distant from the club such as Moyes, Van Gaal and, indeed, Mourinho.
It's worth noting, again, that over both spells at Chelsea, Mourinho spent a staggering £471million on players. EDIT: And by the way, Carragher is a pundit who is supposed to give his opinion on these matters so pretending he's lying because he might have some deluded idea that his opinion will sway the United boardroom is ludicrous. What would be worse for Carragher than to say Mourinho will be a bad move and then watch as the man wins title after title for United? Of course he won't want that to happen.. United's fans will never live it down. If he says he thinks Mourinho is a bad choice, then he means it. It's not some kind of reverse psychology.