Accepting a PhD offer from my tutor's/adviser's "rival"?
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).