Actually, it is kind of interesting looking at the difference between Thrall's Horde and Garrosh's Horde, which is primarily in their opinion of the Alliance.

Let's use Mitawa's post as a starting point, with the New Horde having settled down in inhospitable territory and built new cities only a couple of years prior. When this Horde, primarily the orcs in it, interacts with the Alliance, the human attitude is much like Sinthar described: "You Horde are barely civilized savage murderers that invaded and killed us without reason or warning!"

Thrall's attitude is basically "They're right. It may not have been us, specifically, but we still need to make up for the crimes of our people and prove to them that we have changed." So even if the Horde needs resources, as they did pre-Cataclysm, Thrall wants his people to suffer through it because the alternative would be to go to war with the Alliance, and Thrall doesn't want that because he wants peace with the Alliance and the orcs, as the Old Horde, have already done much harm to the humans. This attitude basically sends two messages to his people: that they need to suffer penitence to prove themselves to the Alliance, and that they shouldn't take pride in being orcs, because, just by being an orc, they share responsibility for the crimes of the Old Horde.

A large part of the reason Thrall is so concerned with the Alliance here is because he really wants to make peace with humans and the Alliance. However, Garrosh doesn't see any benefit the Horde would gain from peace with the Alliance that they wouldn't get from war with the Alliance - in fact, trying for peace is already causing the orcs to suffer from trying to prove to the Alliance that they have changed. And since Garrosh sees no point in making peace with the Alliance, he sees also no point in any suffering the orcs are going through for the sake of the Alliance, and therefore is also telling the orcs that they don't have to be ashamed of being orcs. Yes, the Old Horde did terrible things, but they aren't the Old Horde; they don't need to pay just for being born an orc.

This is where Garrosh's popularity as a leader (as opposed to a warrior) comes from; not only does he say the Horde doesn't have to suffer from lack of resources anymore, he also says that they can take pride in being orcs again.

Here's a speech Overlord Krom'gar gives to his soldiers in Stonetalon occasionally, and while Krom'gar turned out to be the worst kind of orc, I think it's interesting to see why he respects Garrosh and what, precisely, he evokes to try to rouse up his soldiers:

Overlord Krom'gar says: Grunts, ATTENTION!
Overlord Krom'gar says: I am perplexed. Troubled by what I witness...
Overlord Krom'gar says: How has our revered Warchief failed you?
Overlord Krom'gar says: Your families no longer starve.
Overlord Krom'gar says: Your loved ones live with shelter over their heads.
Overlord Krom'gar says: You may walk through the streets of Orgrimmar with pride!
Overlord Krom'gar says: We are the new Horde, and under Warchief Hellscream, we are masters of our own destinies.
Overlord Krom'gar says: WHY THEN, have we failed to take Stonetalon Mountains?
Overlord Krom'gar says: How have the Alliance been able to halt the great Horde war machine?
Overlord Krom'gar says: From this day forth, failure is no longer an option.
Overlord Krom'gar says: Under Hellscream's watchful guise, live or die, we take Stonetalon.
Overlord Krom'gar says: Do not falter, for Hellscream's eyes are upon you all!