'The Second Coming' was written just after WW1 had finished, but the fighting still carried on in Ireland, and the communist revolution in Russia had just occurred. Yeats seemed to take all these events as signs that the Christian ear was coming to an end and the birth of a new god, the poems poses the question of what form this new god will take. At the time the 'Wild Swans at Coole' was written, Yeats had proposed to Maude for a second time and been refused for a second time and some of Yeats’s friends had been executed in the Easter Rising of 1916. so, understandably he was depressed at the time.
'Wild Swans at Coole' has a rhyming pattern (ABCBDD) and a consistent number of lines in each stanza. This predictability of pattern and numbers, I think, represents the predictability of the swans, the fact that they always come back to the same place at the same time, and the consistency of their numbers, there are always 59. whereas, on the other hand, in 'The Second Coming' there is no rhyming pattern at all and no fixed number of lines for each stanza. This emphasizes the unpredictable future that he is writing about, no one knows who, what, how or when this new god or beast will arise.
The themes and moods of the poems are very different, Yeats has chosen his words very carefully to emphasise the mood. 'The Second Coming' has a very depressive, apocalyptic and dramatic mood, the repetition of ‘turning’, repetition of ‘cannot’, the imagery of ‘the beast’, and phrases such as, ‘mere anarchy’, ‘blood-dimmed tide’, ‘passionate intensity’, ‘revelation’, ‘spiritus mundi’, ‘darkness drops again’, ‘stony sleep’ and ‘vexed to nightmare’ create this mood of intense tension between Yeats and the world. 'Wild Swans at Coole' has a very different mood, it is serene, reminiscent, and melancholic. The images of ‘autumn beauty’, ‘the dry woodland paths’, ‘brimming water’, ‘great broken wings’, ‘brilliant creatures’, ‘twilight’, ‘companionable streams’ and ‘drifting on the still water’ create this mood. 'The Second Coming' uses frequent semicolons to give the reader a sense broken sentences to emphasise the image of a broken world, it uses present participles, the repetition of the sound ‘ing’, it creates a giddying tension, preparing the reader for the terror ahead. Whereas, in 'Wild Swans at Coole' Yeats has used colour and prosaic objects to enhance the natural images of autumn and the swans.
These two very different poems have different themes, styles and techniques. Yeats uses lots of different techniques to get his point across to the reader.