According to Ibn Ezra on Devarim 21:15, שניאה is an adjective while שנואה is a noun. When the verse says:
If a man has two wives, one a loved one and the other a hated one
Ibn Ezra is saying that "loved one" and "hated one" here are nouns -- that's the woman's "title", so to speak. It's a statement of fact about her. The word here is שנואה. On the other hand, at the end of the verse it uses שניאה, an adjective, to describe the man's feelings for her:
...and the firstborn is to the one who is hated
Ibn Ezra cites, as support, verses 11 and 14, which talk about the man's desire for her and him no longer delighting in her -- statements about his feelings.
Apparently (I learned while looking this up), Ibn Ezra is disagreeing with a rabbinic tradition (Yevamot 23a) that says that "hated" means the relationship is hated by God, i.e. that this is a forbidden relationship and the man shouldn't be involved with her. The g'mara seems to take as given that "loved" and "hated" mean by God rather than by the man, and does not discuss the use of the two different words here.
Thanks to DonielF for pointing me in the right direction. Any errors are mine, not his.