Most of my points have already been posted individually by other posters, but here is my opinion about Giro/Tour vs Tour/Vuelta:
1) Firstly, as has been pointed out, most GC riders come into the Tour fresh, having spent the better part of a year building up for it, doing whatever it takes to be in the best possible form. A top GC rider, even if he does win the Giro, will already have a hard GT in his legs coming into the Tour.
In contrast, by the Vuelta, most GT riders anyways have a season of racing in their legs including one GT. Furthermore, very few GT riders build their season around the Vuelta.
2) Secondly, the Giro is a more prestigious GT than the Vuelta. It has a long and rich history and is considered a more important GT by nearly all long-term cycling fans (something cycling newbies often forget).
3) Thirdly, partly because riders and teams are more fresh and partly because the parcours are so hard, the Giro is a harder and more tiring race than the Vuelta. And, as has been pointed out, to come into the Tour tired is much more dangerous than coming into the Vuelta tired.
4) Fourthly, every stage is raced hard in the Tour - meaning, the flat and hilly/rouler stages in the Tour are raced much harder. This is especially true due to numerous interconnected factors; a) teams and sponsors care much more about a Tour stage victory than a Vuelta victory. b) There are many more top sprinters in the Tour than Vuelta (this is also perhaps true of the Giro). c) Teams are significantly better for the Tour. We often forget that even domestiques often spend the season building their form to make the Tour team. The Tour team is carefully chosen and each rider is handpicked. d) There are more stronger teams in the Tour - none of those random (Spanish) teams and riders.
All this means that every stage in the Tour is raced full out and is more competitive than the Vuelta.
5) There is also the fact that in general the parcours of the Giro is harder than the Vuelta.
There are also other points, but I don't have enough time now to elaborate.
And then, in terms of Froome, there are several additional factors.
1) He really, really enjoys the severe heat, having grown up cycling in Southern Africa.
Quote from Froome in today's press conference: "The sweltering heat, that suits me."
In contrast, he doesn't like cold weather, and certainly not the snowy conditions of the Giro
2) He really enjoys the Vuelta. He likes riding it, like the atmosphere etc.
Quote from Froome in today's press conference: "Just to come back here, it’s great. The sweltering heat, that suits me, and it’s a great atmosphere out on the roads. The Spanish really get behind all the riders, not just the Spanish ones, even the foreigners, they appreciate a good, aggressive race, and that’s exactly what the Vuelta is.”
He really likes the Vuelta, and that makes a big difference for a rider. In contrast, he thoroughly dislikes the Giro, having been thrown off the race the one time (that I know of*) that he raced it.
*EDIT: He actually has raced it twice