I would say the biggest performance gap between the audio and the Peter Jackson movies is that between Stephens and Viggo Mortensen. Stephens' Aragorn is tough, damaged, wise, and (as far as we can tell) not even particularly good-looking. He carries every scene he is in, and invests dignity and authority in every line, be it Tolkien's original words or new material from Bakewell and Sibley. (And unlike the Peter Jackson films, Aragorn's story is left pretty much intact.)
The gap between Peter Woodthorpe and Andy Serkis is smaller but it is still in Woodthorpe's favour. Gollum's internal dialogue (ie his habit of talking to himself) works well for audio, and indeed here we get a number of extra scenes with Gollum's adventures away from the main storyline. In his penultimate scene, told by Frodo that he can never have the Ring back, he complains bitterly that "nassty hobbitses doesn't realise how long 'never' is", a moment where he almost engages our sympathy. His final moments shortly afterwards are gorgeously manic and rightly expanded considerably from the few lines Gollum's demise gets in the original text.
I remember a few years back seeing an archive interview with Tolkien where he stated with an air of elderly innocence that the books were all about Death. I wondered about this at the time, since to an extent I still read the book through my own nine-year-old eyes, and it's not such an obvious concern of the Peter Jackson films. But it's clearly a theme of the audio. Boromir's funeral, to a minor key variation of the theme tune; Denethor's suicide; Frodo and Sam facing up to death in Mordor (rather than bickering); Bilbo gradually slipping into old age; not to mention the various actual battles; these are all real and awful events in the BBC version. And the music is good, too. It is truly gripping. Get it if you can.
(The Jackson movies do score over the BBC in some respects, of course. New Zealand is a major star of the screen version; also the other members of the Fellowship not mentioned above are given more characterisation and a bit more to do. Though that is sometimes at the expense of the integrity of the story.)