I greatly appreciate your comments.

There is no difference in nuance - they mean exactly the same thing. They are both good formal English too - neither of them is colloquial. The only thing I would say is that you need to say "feel a sense of obligation", not "feel sense of obligation".

Thank you very much for answering. I made some example sentences, I don't still see the differences though. I'd appreciate if you'd let me know which one these are more sound colloquial. 1. I felt obliged to ride her home in return for her kiss. 2. I felt sense of obligation that I should ride her home after she gave me a kiss. 3. I always feel obliged to splash water after my dog taking a pee. 4. I always feel sense of obligation that compels me to splash water where my dog takes a pee while we are out walking.

They end differently, so they would be used differently. Got an example? . I feel a sense of obligation to register my dog. I feel obliged to register my dog. . I feel a sense of obligation that compels me to register my dog. I feel a sense of obligation that won't go away. I feel a sense of obligation that should I not register my dog, I'll feel guilty for a whole day.

No. It can depend on the context and though.