Answer
It depends on what knowledge they have. If they are on the same level, then probably nobody would win. Plus, usually "a win" is not a purpose in this kind of debates, but rather sharing your believes and more learn about other religions, faiths.
A discussion between an atheist, an agnostic and a theist should not be characterized as a battle. There would be no "winner" since the issue is one of belief for certain of the participants and not based on any proof or even a preponderance of evidence. They could discuss and share their various beliefs and philosophies but there could be no bond fide "winner". The problem lies in characterizing each position as an adversarial one. The question fails to acknowledge all the thousands of different systems of belief that have evolved along with humankind. None is the winner and yet they are all winners according to those people who have adopted them. However, when people think of differences as a battle there could be no winner unless someone resorts to the violence which we have seen throughout history waged by people of one religion against another.
The main difference between an agnostic theist and an agnostic atheist is that an agnostic theist believes in the existence of a higher power or deity but acknowledges that it cannot be proven, while an agnostic atheist does not believe in a higher power or deity and also acknowledges that it cannot be proven.
He is a theist - he describes himself as a Muslim.
She is catholic.
An agnostic atheist is someone who does not believe in a god or gods but also acknowledges that the existence of a god cannot be proven or disproven. An agnostic theist, on the other hand, believes in a god or gods but also acknowledges that the existence of a god cannot be proven or disproven.
I presume you mean, Richard Branson. He is an atheist.
Richard Dreyfuss has described himself as a believer in God, but does not affiliate with any specific religion. This would classify him as a theist.
Atheist - If he is sure there there is no specific god because of the impossibility and/or improbability of his existence. Agnostic - Not sure whether there is a god or not. Usually does not care. An atheist is the opposite of a theist. The theist believes there is evidence for the existence of their favorite god. The atheist does not. It would be illogical for the atheist to "deny" the existence of something for which there is no evidence. Atheism is merely the lack of a belief. Knowledge is absolute. Since nobody can know with absolute certainty no gods exist, everyone is agnostic. So the so-called "agnostic" has the same lack of knowledge as the atheist or theist has. It's just commonly accepted that an agnostic does not commit either way.
These are fine distinctions, but some philosophers define a range of beliefs: Thiest - certain that god exists. Weak thiest - acknowledges that one can't be certain, but believes. Agnostic - neither believes nor disbelieves. Weak atheist - acknowledges that one can't be certain, but disbelieves. Strong atheist - certain there is no god. As you can see, "weak atheists" hold the middle ground - in fact, most atheists are probably weak atheists - they acknowledge that certainty isn't possible, but it is very unlikely that god actually exists.
He an anti-theist (against religion) but more-so agnostic when it comes to the existence of a so called "God".
Just ask them if they are atheist, theist or agnostic. most won't be ashamed to tell you. However if they don't agree with your simple 3 category breakdown you might get an answer like None of those, Secularist, pagan, Rastafarian, Epicurean, Stoic, Freethinker, etc. You will then have to shuffle your categories.
A non-theist is someone who does not believe in a specific deity or god, while an atheist specifically denies the existence of any deity or god.
The opposite form of atheist is theist.