Different effect of Harry's Cruciatus curse at Ministry Skirmish vs Battle of Hogwarts?

Question

In HP & the Order of the Phoenix, Harry chased Bellatrix Lestrange after she murdered Sirius Black. He used cruciatus curse on her but it was not really effective.

As Bellatrix said:

"You need to mean them, Potter! You need to really want to cause pain... to enjoy it... righteous anger won't hurt me for long... I'll show you how it is done, shall I? I'll give you a lesson —"

Later when Amycus Carrow spat on Minerva McGonagall, Harry used the curse splendidly.

As Amycus spun around, Harry shouted, "Crucio!"

The Death Eater was lifted off his feet. He writhed through the air like a drowning man, thrashing and howling in pain, and then, with a crunch and a shattering of glass, he smashed into the front of a bookcase and crumpled, insensible, to the floor. "I see what Bellatrix meant," said Harry, the blood thundering through his brain, "you need to really mean it."

Harry Potter Wikia attributes this to lack of sadistic feeling in Harry.

But still it makes no sense. Harry should have had more desire to cause pain after murder of his godfather but he was only able to knock Bellatrix off her feet. Wikia however also suggests that Bellatrix was probably less affected by the curse due to her lack of conscience and being a sadistic person herself but somehow I don't feel it's quite right.

Only rational explanation that I have been able to give myself is that the war-time environment changed Harry Potter from a young boy he was in HPTOOTP to a grizzled veteran by the time of Battle of Hogwarts & somehow his sense of emotions was also affected by it.

Could it be that Harry liked McGonagall better than Sirius and thus was able to channel his anger better than he did in Ministry skirmish? Is there any better explanation?

Answer 1

I think you basically answered your own question. It's not about who he cared for more, it's about his emotional state. When Harry attacks Bellatrix, he's fifteen, angry, scared and shocked. He's an emotional wreck.

"SHE KILLED SIRIUS!" bellowed Harry. "SHE KILLED HIM I’LL KILL HER!"

Later

"Aaaaaah... did you love him, little baby Potter?"

Hatred rose in Harry such as he had never known before; he flung himself out from behind the fountain and bellowed, "Crucio!"

The reason his spell doesn't work is exactly as Bellatrix says - you have to mean it. Harry can't truly mean it in this state, he's too confused, too upset, and at that age, too good to enjoy someone else's pain the way the Bellatrix could. He tries because of righteous anger, not because he would truly enjoy Bellatrix's pain.

Compare this with when he attacks Carrow.

Harry pulled the Cloak off himself, raised his wand, and said, "You shouldn't have done that."

As Amycus spun around, Harry shouted, "Crucio!"

This is far calmer, almost premeditated. He's cool enough to deliver a line, and cool enough to control his own actions. He chose to hurt Carrows, not just out of righteous anger, not out of impulse, but because he wanted to see him suffer.

It's the difference between temporary insanity and premeditated crime. It's not more passion that makes it worse, it's less.

Answer 2

Your rational explanation is correct. As I referenced in THIS answer, the words themselves are only a template of the spell, providing a focus point for the mind. Using references from the books:

• When HP enters the Floo Network, thinks about going to Diagon Alley, but says "diagonally", He shows up in a fireplace in Knockturn Alley, which is diagonal from Diagon Alley.
• When Crouch-as-Moody is teaching the Defense vs Dark Arts, he mentions that the students "get your wands out and point them at me and say the words, and I doubt I'd get so much as a nosebleed" in reference to 'Avada Kedavra'... because the will to kill isn't there; Similarly, when the Moodyganger is showed using the Cruciatus curse on the spider later in the book (or when HP uses it on a Death eater in the final book) it is both through the words and a torturous intent.
• Also in Goblet o'Fire, when HP uses Accio Firebolt, it does not bring any nearby Firebolt, nor does it bring every Firebolt nearby, but specifically Harry's personal Firebolt that he was concentrating on.
• When HP uses Sectumsempra, he knows the exteremly simple jist of the spell - It's for Enemies. Being able to concentrate, using the wand as a focus, HP directs the spell towards his enemy, not knowing what will happen. It's the magical version of "Stick 'em with the pointy end".
• The closest we get to magic metaphysics is the discussion surrounding the Patronus charm. Lupin says directly, "With an incantation, which will work only if you are concentrating, with all your might, on a single, very happy memory". There are direct discussion referencing how it has to do with mental state, showing HP eventually succumbing after a dementor assault; it also may have something to do with inner morality, as the only Death Eater to show the use of one is Snape. The incantation for the patronas may be Incorporeal or corporeal, but it has to do with the mental state, not the actual incantation.

Although he had been told BY Faux-Moody the previous year that the hateful intent is the key to the Unforgivable Curses, he isn't filled with hate or sadistic intent. While it's not really known if he likes McGonagall more than Sirus, he certainly had more time and contact with her on a literal daily basis. Add that to the fact that that he's been required to be an increasingly deadly force through the story, it doesn't surprise me at all that he had some pain to channel. Between the two incidents, dozens of people he knew had died, including Hedwig, Dumbledore, the Real Moody, and (if I have my timing right) Fred Weasley.