Poked that troll's blog again for the lulz, and ended up thinking of a comparison not long after. What's the difference between Jesus's resurrection and the Roswell alien incident? Not a whole lot where I stand.
1) Believers cite "eyewitness testimony." Eyewitnesses are notoriously unreliable. That's why science relies on forensic evidence whenever it's available. Eyewitnesses can lie. Eyewitnesses can misremember. Eyewitnesses can misinterpret what they see and adjust their memories to line up with what they thought happened. Of course, if some woo shows up, they're going to misrepresent that as me saying those eyewitnesses were crazy. Not necessarily. Those are perfectly normal mortal failings. Our brains evolved to survive, not to arrive at scientific fact or to objectively record what we see like a celluloid camera is. They've been (a little more than) good enough to ensure we've got food in our bellies and safety from predators. That's why we rely on objective, verifiable scientific evidence and not subjective memory.
2) Believers cite "eyewitness testimony" recorded long after the event. Do I really have to go into this? I remember one show that was about debunking Roswell. They had a group of people escorted by a faux group of military people while wearing helmet cameras. One month later, they were talking about being lead past unknown equipment, and one said a guard raised his rifle at him. The cameras, meanwhile, played back showing only trees and calm guys in uniform. Now imagine someone making claims decades later. Now imagine someone writing down about what someone else said centuries earlier, and can't even get straight who was there. Now imagine the possibility that those people doing the writing want you to buy their book or go to their church.
3) Believers typically already buy into unfalsifiable magic. Jesus, like all magic men, has a Green Lantern Ring. Aliens have Do Anything Robots and equally flexible spaceships. There's no limits to the powers people will invoke to explain anything, while failing to explain why it didn't happen another way. The eyewitnesses to these things typically don't understand anything about how the universe works, but they believe in magical things that can be invoked to explain anything, be it super-aliens, omnipotent men in black, angels, or spirits. So, if these people see something they can't explain, instead of seeking out known explanations for the phenomena, they'll just immediately jump to "magic." It doesn't help that there's no shortage of fantasy-prone people, especially if you live in a culture that values "visions" or "repressed memories."
4) Believers expect us to make special exceptions to logic for their case. Conspiracy nuts often ask me to just throw away Occam's razor and not talk about evidence for aliens because the MIB covered up all the evidence to make it look exactly the same as if it never happened. And that this new entity leaves no evidence of its own. For Jesus, they expect people like me to believe that the religious people who allegedly saw the resurrected Jesus were somehow more special and more objective than all the "witnesses" to non-biblical miracles and magic throughout the centuries, and thus we should throw out all the questions we'd ask about the incident we would ask for any flying saucer cult's claims.
There's probably a lot more. I might expand this post, depending on comments. Scientology tag included just because there's not too much difference between them and the standard alien nuts. That and it might provoke some painful thoughts in the Christian fundies who don't want to be associated as equals with them.