Well, I think our actual senses (sight/sound etc) are probably getting equivalent data, but that there's something different going on at an unconscious level beyond our control(*) (where our brain decides what it important enough to bring to the attention of the conscious mind)

Similar to the way that say someone with depression might tend to interpret everything in a negative light (even if they try to interpret things differently). Which sounds like I'm saying religious people are mentally ill, but given that atheists are in the minority it makes more sense to say we are(**), and anyway just because people with depression may not function very well by conventional standards doesn't mean they're wrong.

(*)Or at least, largely beyond our control.
(**)A very unpopular atheist opinion :D