How does the content differ between radio and book versions of The Hitchhikers Guide?

The first two seasons - ie the originals, which Adams was actually involved with - are quite different to the books. The first season actually came first of all, and includes parts - although nowhere near all - of what became both the first and second books. The second season only has occasional similarities to the second book, with large amounts of completely different material (Lintilla and Poodoo appear nowhere in the books, for example). Adams was actually proud of the fact that the books and radio series totally contradicted each other.

Those two series were made in the 70s/80s, but after that no more were made during Adams' lifetime. Much, much later - in the mid 2000s - the BBC decided to commission adaptations of the three other books. Naturally, since Adams was no longer around, the adaptations were much less free - although some material was new, the bulk is the same. This is why there's a total jar at the beginning of the third radio series - to get the story back on track with the books, they had to dismiss all of the diverging continuity as a dream.

It's definitely worth reading the books. You won't miss much in terms of continuity if you don't, but they're hilariously funny in themselves, and of course contain a lot of both story and humour that didn't make it into the radio versions.