The biggest similarity that we can identify beween these three classic poems by Gerard Manley Hopkins is the way in which they all focus on nature as beautiful and as a reflection of God's beauty. Thus Hopkins writes of the way that seeing a kestrel fly inspires him to praise God for how wonderful He is and the genius of his creation, and we can see the same ideas coming forth in "Pied Beauty." Nature for Hopkins was a lense through which one could see the love, beauty and order of our creator God more clearly and appreciate his genius and the wonders of his creation more keenly.
All three of these poems use sprung rhythm in the way that Hopkins does not write in a conventional meter and adopts an almost conversational tone in his poems. The use of compound adjectives such as "dapple-dawn-drawn" is another stylistic feature of his work, as is the utilisation of alliteration, such as "Brute beauty" and "swift, slow; sweet, sour." We can therefore see that there are plenty of similarities in these poems.
The only difference I would argue is to be found in "As kingfishers catch fire," which, although it uses nature to start off the poem, is actually a philosophical meditation on man and his role in life and describes what a good man is:
I say more: the just man justices;
Keeps grace: that keeps all his goings graces...
This is a different focus compared to the other two poems that very much take their subject as nature and the thoughts and feelings that such sights as a kestrel flying inspire in the poet.