Arithmancy was a very different subject from Divination
You're right to say that Hermione saw Arithmancy as her favourite subject. She continued studying it right up to her sixth year. However, her explanation of why she loved it so much was - tantalisingly - interrupted by Ron's discovery of Scabbers's faked death.
“Why don’t you just drop a couple of subjects?” Harry asked, watching her lifting books as she searched for her rune dictionary.
“I couldn’t do that!” said Hermione, looking scandalized.
“Arithmancy looks terrible,” said Harry, picking up a very complicated-looking number chart.
“Oh no, it’s wonderful!” said Hermione earnestly. “It’s my favorite subject! It’s -"
But exactly what was wonderful about Arithmancy, Harry never found out. At that precise moment, a strangled yell echoed down the boys’ staircase. The whole common room fell silent, staring, petrified, at the entrance. Then came hurried footsteps, growing louder and louder - and then Ron came leaping into view, dragging with him a bedsheet.
(Prisoner of Azkaban, Chapter 12, The Patronus).
It's clear, however, that it wasn't the prophetic aspect of Divination that Hermione had a problem with. She expresses no scepticism whatsoever about the concept of prophecy when Harry relays the contents of Trelawney's prophecy to Dumbledore; she takes it at face value. She has no problem with the notion of predicting the future using magic. She even goes as far as to defend Divination against Ron's scorn after she comes across legitimate prophecy.
"Bet Dumbledore wishes he could've got rid of Trelawney for good," said Ron, now munching on his fourteenth Frog. "Mind you, the whole subject's useless if you ask me, Firenze isn't a lot better..."
"How can you say that?" Hermione demanded. "After we've just found out that there are real prophecies?"
(Order of the Phoenix, Chapter 38, The Second War Begins).
It seems to be partly Trelawney's classroom methods that she objects to.
“Professor Trelawney said you didn’t have the right aura! You just don’t like being bad at something for a change!”
He had touched a nerve. Hermione slammed her Arithmancy book down on the table so hard that bits of meat and carrot flew everywhere.
“If being good at Divination means I have to pretend to see death omens in a lump of tea leaves, I’m not sure I’ll be studying it much longer! That lesson was absolute rubbish compared with my Arithmancy class!”
(Prisoner of Azkaban, Chapter 6, Talons and Tealeaves).
That conversation is the only time that we hear Hermione directly compare the two subjects. It seems that she believes that Divination involves making things up whereas Arithmancy has a more precise, objective, rational methodology. Additionally, she had something of a personal feud with Professor Trelawney, which she didn't have with Professor Vector.
Some further supplementary reasons why Hermione may have liked Arithmancy include: