I’ve been recently rewatching (and enjoying) 30s monster movies (Frankenstein & Bride, The Invisible Man, etc.) I can say 100% that the romance scenes are never as cheesy as the AOTC ones. Sometimes it’s a bit on-the-nose, but it’s charming rather then grating (tho I will say, the romance in The Wolf Man hasn’t aged well, due to the social conventions of the time).

The performances play a part of it too. Claude Rains eats up his power-hungry monologues as Jack Griffin as much as James Earl Jones does as Darth Vader OT, and his scenes with Gloria Stuart are flowery but charming. Both Rains and Stuart were theatre actors, and thus knew how to pull off compelling melodrama. Same with Colin Clive as Henry Frankenstein and the two actresses that played Elizabeth.
Meanwhile, it feels like Hayden Christensen and Natalie Portman are uncomfortable with the dialogue. They’re not experienced with that theatre melodrama, so it’s just awkward.
It’s also why Ian McDiarmid and Christoper Lee fare better with their material. McDiarmid is a theatre actor and Lee was basically reprising his role as Dracula.