I do not agree that Garrosh is a competent military commander. The few cases we've seen him make military decisions, they've been resoundingly bad and caused more damage to the Horde than benefit. I would wager his upper leadership is the source of the majority of his successes.
The best example of Garrosh's command would be the Twilight Highlands intro. In the space of one rash, bullheaded, egotistical command to send his fighters to harass the Alliance armada in the area he succeeds in losing his entire air force to the Twilight Cult, nearly gets himself killed, and has his entire navy decimated by the Alliance counter-attack with their superior naval strength in the region.
Not a competent commander.
His behavior and attitude has also convinced a lot of his commanders to be extremely into the dark end of the spectrum because he makes it sound okay. Yes, he killed the Commander for destroying the Cenarian Circle school, but he also set the precedent and mindset in his people that such acts were okay in the Horde now through his behavior and rhetoric.
To counter this, in The Shattering, he is shown to have done something few Orcs would even consider. He prepared for a backup plan incase they lost. Garrosh, throughout Wrath, became a competant general. More than, that, he became a pretty damn good one.
So what changed? Leadership. In Wrath, Garrosh worked under Saurfang, who was (and is) in fact, a damn good Orc. Garrosh had someone else to make the important decisions for him. Not tactical or strategic decisions, but the ethical ones. As Warchief, He's still a competant general, but his own inflated pride and need to stroke his massive... Mamoth tusks, lead him to making terrible decisions because of a total lack of ethics. We started to see this when he butted heads with Cairn. Had Garrosh not been the defactor leader of the entire horde, viewing himself as above everyone else, he probably would have listened to the old bull instead of killing him,
He's not a 'real' Orc, either. Without someone to keep him morally grounded, he is more Legion-Orc than Real-Orc. The Orcs, prior to thier corruption, were tempered, thoughtful and not particularly rash. They avoided serious conflict whenever possible, and didn't even seem to have a concept of conquest.
Garrosh is everything Thrall and more importantly Grom worked so hard to rid the Orcs of. THATS why he's hated, and he rightly deserves to be. If daddy were still around, he'd smack the brat upside the head.