The Nature and IVs of the Legendary will be completely random, just like the first encounter.
EDIT: Now that I think back to the ol' Platinum, I think the above answer is flawed. You have no way of knowing what pre-E4 Kyogre is, so there is no way of proving that the post-E4 Kyogre is or is not the same (Note that Synchronize is not a 100% reliable way of proving this theory, as it only has a 50/50 chance of working).
2nd EDIT: Now that I think about it more, my experience in Platinum was most likely a fluke. This is because if you SR the Legendary after the E4, it will have random stats each time you encounter it. Therefore, it will not have the same stats as the first time you encountered Kyogre.
So I guess my answer is definitely no.
TL;DR No, it will not have the same stats/nature as before.
Sorry for the confusion!