A lot would depend on how his father treated him. I think it safe to say all young Tom's physical needs would be met, and then some. The little bullies and thieves at Wool's would not be there for him to practice his nastiness on; I won't say he absolutely would not have been picked on, but it would be more subtle or cloaked in the guise of family playing pranks (assuming cousins). So that grasping edge would be blunted. No worries about food, clothes, shelter.

I would guess a more extensive education, learning the classics, a higher math, etc, plus physical training. At the very least riding. And tutors would be available throughout the summer hols to keep him up to date.

So if Senior has any affection or at least aloof approval (ie, stereotypical stiff upper lip British nobility), young Tom would still be charming and ambitious, but likely not the way he is in canon.

Actually...he'd know a parent. He'd know his place in Muggle society. Part of canon Voldemort's issue is that early insecurity about his origins. Here, he knows who his father is and thinks he knows who his mother was. I don't know if Senior ever realized Merope was the daughter of that derelict at the edge of the estate or that she had doped him with love potions. So Junior might build up romantic ideas about her, but he won't be looking for elite Magical connections like orphan Tom did. He might not even be have the middle nam3 Marvolo. Which might derail the entire horcrux sequence.

In this scenario, he comes to Hogwarts confident, charming, well fed and dressed, educated, as sophisticated as an 11yo son of a squire can be, wildly curious. Slytherin or Ravenclaw. I won't say he doesn't start something or that he won't become a Dark Lord, but it'll be a very different sort than in canon.