I looked it up notably on wikidiff, but the difference is barely noticeable: both words essentially mean blessing, it seems. That's also what most dictionaries say.
The meanings are, as you say, identical.
The only difference between them is that most people have never heard the word benison. I've only ever seen it in The Canterbury Tales and in the poems of the "war poets", who were unusually fond of the word. One of them, Wilfred Owen, also uses its opposite: malison:
Yet, for men's sakes whom thy vast malison/Must wither innocent of enmity
Malison means 'curse'. Benison means the opposite: blessing.