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The difference between the two is mainly focus. In ‘Sie besprechen den Plan’, the focus is on the plan they are discussing. Maybe they already know rather clearly what they want and just have to hash out the details.
In ‘Sie besprechen sich über den Plan’, the focus is put more on the discussing people themselves or the discussion itself and less on the plan. Maybe they need to argue a lot, because they have different ideas on what the best plan could be.
I don't know why DUDEN lists besprechen as a reflexive verb. It is not used as such. Hence, the second sentence you gave for an example doesn't sound correct to me. You can say: "Sie haben eine Besprechung über etw." oder "Sie sprechen sichab" but not "Sie besprechen sich über den Plan". This verb is only used as a transitive verb.