There's not an awful lot of direct contradiction between the two IIRC, because the one looks a the politics of the situation and the other at the level of individual soldiers/sailors/airmen.

I know that Darkest Hour gets a lot wrong about it though, in service of its hagiography of Churchill - in particular his involvement in the planning.

• The use of "little ships" is one of the enduring myths of Dunkirk anyway, with the vast majority of them being requisitioned and manned by Navy personnel and only a few being sailed by their own civilian crews. Dunkirk, like its predecessor the 1958 John Mills movie, emphasises the role of the civilian crews because that's the better story.

• However, the requisitioning of the little ships wasn't come up with by Churchill mid-crisis, but was one of a number of contingency plans put together by the Merchant Navy at some point before the war and enacted by the Small Craft Section of the Ministry of Shipping - a ministry created only in wartime.

• The other major one was that the "Fight them on the beaches" speech was given as a response to the defeat of Dunkirk on 4 June, the day the last soldiers returned. Here is the full text of the speech in which Churchill post-mortems the Dunkirk campaign to the House, celebrating the deeds of the various arms involved but warning that "wars are not won by evacuations", before going on to the question of "so what now?". In Darkest Hour, however, the speech is presented as having been given mid-crisis with a different aim of forestalling a (historically non-existent) vote of no confidence.

• Finally - though a more minor point - the speech itself wasn't broadcast on the radio: unlike many of his other famous ones, it wasn't later re-recorded for broadcast but the "soundbites" read out by a newsreader. So Clemmie, the King, the secretary and anyone else not in the House of Commons at the time, wouldn't have heard it.