Accepting a PhD offer from my tutor's/adviser's "rival"? Last year, when planning my academic future, I contacted a research group at my university, because I was interested in doing my Master's thesis in their field. One of the professors replied a couple of days later, and offered me a meeting. After said meeting, I accepted the proposed project, and have been working on it since. A few days after accepting the project I received another reply to my initial mail, from another professor in the group, which turned out to be one of my teachers in a course I had a few months after. I stayed with the first professor and project.

So fast-forward to present day: I am finishing up my Master's thesis, and interested in pursuing a PhD. I have not talked about it with my current adviser, and he hasn't offered me any projects (he is actually going to MIT in June, for a sabbatical, so he will be absent for a year). A couple of days ago, while talking with the second professor, he offered me a PhD scholarship/fellowship (I do not know the right word). The precise field of research has not yet been decided, because it depends heavily on government funding (but the general area of research is of interest to me). I have recently learned that said professor is actually a sort of "rival" to my current adviser (they have had projects from rival companies, and had a "competition" over an academic position).
I do not know whether to accept or not. I like the offer and the professor, but I would be interested in staying in the research group after completing my PhD, and I think it might offend my current adviser and cause tension.

Is it OK to accept said offer right now (telling my adviser, of course)?
I think that the correct answer is: it depends.

Theoretically, you should be able to accept the offer and tell your current adviser right away. However, practice and theory do not always agree. I know of a case where a student received a lower (but still good) grade for her master thesis than originally was intended, after she turned down the offer to do a PhD thesis with the her master thesis adviser.

So, you will need to assess whether your adviser's ego would be able to deal with you performing a PhD at his rival's group. When you think that this is not the case, or when you are not certain, then it is better to inform him after your master thesis grade has been determined.

Things are a bit different when you actually would prefer to perform a PhD thesis under the guidance of your current adviser. Then, I would suggest that you inquire about such possibilities. You do not need to mention that you have an offer from his rival. 

Finally, I would like to stress that it is your life and academic career, so it is in your own best interest to choose the path that suits you best (and not necessarily your adviser's).