Do you think Joffery would have turned out different if he had been raised elsewhere? Myrcella & Tommen are fine but Joffery is a perfect storm of his parents' vices (Robert is the dad as far as parenting is concerned).
Yes. Different experiences = different character. To what extent, though, that is the question. People have been asking that one for ages and not just in relation to Joffrey.
GRRM clearly intended for some nature vs. nurture debate around Joffrey; not for nothing do we hear about both Joffrey cutting open a cat (past the age he should be able to understand that animals feel pain, as far as I can tell), and hear the response was Robert hitting him so hard he lost a tooth, and see that Cersei by and large had no problems with Joffrey’s behaviour. Not for nothing are both Myrcella and Tommen good kids.
It’s all meant to lead back to the question: is Joffrey inherently bad?
At the very least, I think the scales were grossly weighted in favour of him turning out cruel and spoiled, right from the day of his birth. Between whatever genetic or psychiatric issues we’d call “nature,” the exalted heir apparent position he was born to, and his parents’ neglect/overindulgence/abuse…it’s a bad stew to raise a child with. (And whatever’s gone wrong at whatever point, GRRM doesn’t let the reader forget that Joffrey was a child, as he depicts Joffrey dying confused and afraid in his mother’s arms.)
Anyhow. A lot would depend on when Joffrey was largely removed from the influence of Robert and Cersei, and who became a parental figure in their place. To name a few likely substitute parent candidates, I doubt Grandpa Tywin, Uncle Stannis, and Uncle Renly read from the same parenting guidebooks.