"His/her" implies a more personal connection to the object, and therefore we get the sense it is of importance to the character. It's subtle, and many readers may not even notice it specifically, but it contributes to the mood and atmosphere you're trying to build.
If you want to give off the impression that the character is comfortable and relaxed in the place, for example, then you'd say his radio, his bed, his coffee maker that only worked once then gave up the ghost.
However, if you want the space to be more impersonal, then you'd talk about the radio, the coffee mug, the oddly lumpy sofa. It gives more of a sense of distance, and you can even make it so the reader can tell the character feels way out of place without ever having to say it outright.