Ellen Ripley (feats limited to the first 3 Alien movies only) vs. Sarah Connor (feats limited to the first 2 Termintaor movies only).
Round 1: Pure h2h fight in a cage match
Round 2: Each is armed with an automatic rifle, a pistol and a knife. They're then tasked to hunt each other down in a shopping mall.
Round 3: Who's more badass?
I'd go with Sarah in both rounds, by T2 she's spent over ten years training herself to survive Judgment Day. Learning everything from H2H combat, weapons, to survivalist tactics.
More badass, definitely Ripley. She faced down an Alien hive and queen using a forklift, the P-5000 Powered Work Loader.