The two spellings arise from two different systems which have been created to represent Chinese (Mandarin) words using a Romanized alphabet. The Wade-Giles system was developed in the mid-to-late 19th Century and was the main system used through most of the 20th Century. The Pinyin system was adopted by the People's Republic of China in 1979 and has since become the international standard system for modern Chinese. Despite the difference in spelling, both systems are attempting to represent the Chinese word which sounds like "dow" - rhyming with "cow", "now" and "how" - so that's how it should be pronounced regardless of spelling.
For myself however, I first saw the "Tao" version and not knowing any better imagined that the word began with a "t" sound, and hence that's how I began to say it. These days, despite knowing better, I still say the words "Tao", "Taoism" and "Taoist" with a "t" sound instead of a "d" sound. There are three good reasons why I do this....
- One of the central principles of Taoism is that the word is not the thing. The opening lines of the Tao Te Ching are "The Tao that can be named is not the eternal Tao" so getting hung-up on how the word is meant to be said is completely missing the point. Instead of calling it "The Tao", we could call it "The Universal Motivation", "The great Ooohjah", or even "Bob" and still mean the same thing. It's not important and I think it's important to remember this.
- When I was in Shanghai, our guide told us that when the Chinese talk of Taoism using the English Language they say "Taoism" with a "t" when they mean Philosophical Taoism, and "Daoism" with a "d" when they mean Religious Taoism. Now I've not heard this anywhere else, but who am I to argue with him?
- I prefer the sound of the word when it starts with the "t" sound. Of the two, that pronunciation makes me happier.