Like, you can find tons of examples online of Islamic or Christian websites that cobble together evidence that they purport proves the existence of God/their religion, and websites that attack the validity of other religions by dissecting or mocking their beliefs.
Was there anything ever comparable written by the Romans or Greeks?
Yes, yes they did. I will just give one example.
The 2nd century writer Celsus wrote a major contemporary attack on Christianity known as "The True Word" (circa 177 or 78). The work itself has not survived, except in Origen's work "Against Celsus", which quotes Celsus considerably and then offers Origen's own rebuttal of Celsus' arguments.
Celsus does things such as provide an alternative account of Jesus' birth in which his father is a Roman soldier named Pantera, claims that Jesus' miracles were performed by sorcery, and complains that if God were universal, why did he so reveal himself into just one part of the world.
The fact that Celsus' writings did not survive except in a quoted form is, from a historical viewpoint, unfortunate, but that's the kind of situation you are dealing with when reconstructing anti-Christian writings from antiquity.
A really great, accessible book of Roman criticism of early Christianity is here: The Christians as the Romans Saw Them http://www.amazon.com/The-Christians-Romans-Saw-Them/dp/0300098391