Courtney isn't cruel enough to be the main antagonist, so as far as an antagonist goes, she's going to fall behind Heather. Look at everyone's complaints about her: She's ruthless, she's a strong competitor, she's willing to put everyone's lives on the line to get that million for herself.
But ultimately, she doesn't build a power base like Heather. It was quite clear that Duncan was the driving force behind the pair's alliance: Courtney just wants to win. Aside from a few quips to Lindsay, and her fighting with Duncan (as crushes tend to do), she's never out and out malicious to anyone. We don't see Courtney reading Gwen's diary, we never see her angry with Leshawna for her insults (although, to be fair, Leshawna didn't really do that).
Courtney's cut-throat, but ultimately, it wouldn't matter who the other competitors were: she treats them all merely as competitors, and doesn't really relate to them specifically outside of Duncan and Lindsay. Lindsay was pretty nasty to Courtney during their time on Playa de Losers, so it makes sense that Courtney dislikes her. This is in sheer contrast to Heather, who used Trent specifically because it would hurt him and Gwen. She used Lindsay specifically because she was stupid, and Beth specifically because she wanted to be liked by others. Ultimately, Leshawna is just as "alpha female" as she was i TDI and TDA, but we never see Courtney contrast with her like Heather did. To Courtney, Leshawna is just a strong competitor.
Although Courtney is indeed an antagonist, she's, and I'll probably check flak for this, she's an antagonist with an abject lack of malice. She's not going to go out of her way to hurt anyone, unlike Heather.