An uniformed beat cop still is way more experienced and skilled in dealing with dangerous situations than a commenter here. Think about it this way : who would you want to call when somebody breaks into your house, an uniformed beat cop or the HN commenter with the top ranked comment on the another police outrage post? No, the stealth sniper is not available, Jedi knights too.

Assuming somebody has broken in to my house and is presently in the house with me.

Is calling the police the best of all possible solutions in this scenario. How do the police know which one of you is the offender?

The police will probably correctly identify the person fleeing the scene while carrying a tv as the perpetrator. If for whatever reason the distinction is not so easy to make, they can just capture you both and ask your neighbours which one of you lives in your house. And presumably there is some way to prove that you live there, e.g. the house is on your name, there are pictures of you laying around, the dog listens to you, you know the color of the cups in the closets in the kitchen, all the clothes in the house happen to fit you... need I go on?

That assumes that a) the person flees and b) police stop to ask questions.