I have made two self-made similar sentences to find out where one can use each one of the verbs "indebted" and "owe". For me, they both can be used without any change in the meaning in both of the following sentences, though I doubt about it:
- You rescued me and I am indebted / owe to you. [intransitive role]
- You saved my life and I am indebted / owe my life to you. [transitive role]
Do you confirm it? If not, then please let me know why?