- Uhh, the movie makes it repeatedly and emphatically clear that to marry Sab Than is to hand Helium over to a tyrant who also happens to be the leader of its traditional enemy. Dejah ran away explicitly to find another way to save Helium without making it into a client state of Zodanga- it was hardly a case of a Rebellious Princess throwing a tantrum and, upon deciding that marrying Sab is her best (or at least, least bad) option, she does indeed willingly agree to marry him to save her people. Not denying that Book!Dejah is a strong character, but you're really going out of your way to make Movie!Dejah look bad in comparison.
- Zodanga was essentially destroying Barsoom and Sab Than wasn't going to change his ways. Dejah actually said that while this marriage might save Helium it wouldn't save their planet. Although this leads to significant heaps of Fridge Logic: namely you have to wonder how much Mars' resources has Helium used up to be able to fight Zodanga for 1000 years, what 'another way' was Dejah hoping to find, what exactly the conditions of peace would be, oh and there is also the fact that Dejah has invented a device that can potentially restore Barsoom's ecology... That said, the climax has shown very well just why Dejah was right trying her damndest to avoid this option. It was a trap. Anyway, the OP is right in that a female character is only ever considered strong nowadays if she is a Xena clone.
Analysis / John Carter
The movie makers boast they have made Dejah Thoris a 'strong' character by handing her a sword. To start with Dejah is far from weak in the book. Captured by the Tharks she makes an appeal for peace and friendship between their peoples that actually impresses the chiefs. She shows no fear at all, is always up for an escape plan no matter how harebrained, attacks a ten foot Green martian woman who is flashing sunlight in John Carter's eyes as he fights a duel and would have fought and died beside him had he not literally thrown her on a thoat and ordered Sola to get her out of there. Captured (again) by the unfriendly Zodangans she voluntarily embraces marriage to the Prince in order to save her city, insists on standing by her word after John Carter reappears and informs him she could never marry the man who killed her betrothed no matter how she feels about him. Yeah, real weak.Movie!Dejah is so strong and she has a sword but she runs away from the marriage that will save her home to go adventuring with John Carter. Hmmm.