I ran across this helpful analysis by G.K. Chesterton on a forum thread on Monachos.net, posted by Fr Aidan Kimmel.
I argue very forcefully against the 'Same God' position in my book, Facing Islam, in large part because of the radical differences between the True Triune Godhead and the dark and sadistic Allah. Because of these extreme, polar differences, and the aggressive, supremacist, murderous commands issued by Allah in order to subjugate the whole world under Islam, we cannot merely say (as do some Orthodox) that Muslims have the wrong conception of the True God. We must not allow such wishy-washy softheadedness to dilute our dogmatic stance. Rather, there is a stark ontological difference between such a blatantly evil monad as Allah, and the Triune God Who is Three Persons Sharing One and the Same Essence and United in Love. There is also clearly a satanic influence at work which globally compels and enables Muslims to stifle, shut down and kill their God-given conscience in order to follow the grossly evil commands of their 'god' and 'prophet'.
Unitarians (a sect never to be mentioned without a special respect for their distinguished intellectual dignity and high intellectual honour) are often reformers by the accident that throws so many small sects into such an attitude. But there is nothing in the least liberal or akin to reform in the substitution of pure monotheism for the Trinity. The complex God of the Athanasian Creed may be an enigma for the intellect; but He is far less likely to gather the mystery and cruelty of a Sultan than the lonely god of Omar or Mahomet. The god who is a mere awful unity is not only a king but an Eastern king. The heart of humanity, especially of European humanity, is certainly much more satisfied by the strange hints and symbols that gather round the Trinitarian idea, the image of a council at which mercy pleads as well as justice, the conception of a sort of liberty and variety existing even in the inmost chamber of the world. For Western religion has always felt keenly the idea "it is not well for man to be alone." The social instinct asserted itself everywhere as when the Eastern idea of hermits was practically expelled by the Western idea of monks. So even asceticism became brotherly; and the Trappists were sociable even when they were silent. If this love of a living complexity be our test, it is certainly healthier to have the Trinitarian religion than the Unitarian. For to us Trinitarians (if I may say it with reverence) -- to us God Himself is a society. It is indeed a fathomless mystery of theology, and even if I were theologian enough to deal with it directly, it would not be relevant to do so here. Suffice it to say here that this triple enigma is as comforting as wine and open as an English fireside; that this thing that bewilders the intellect utterly quiets the heart: but out of the desert, from the dry places and, the dreadful suns, come the cruel children of the lonely God; the real Unitarians who with scimitar in hand have laid waste the world. For it is not well for God to be alone.