I think that most religious people don't think they are 'wiser'. Not because they are aware of their own illogical word-view but because they effective look down at 'wisdom' as being something inferior to faith. For them, faith is everything. It is greater than wisdom (which is an Earthly concept and a conceit); it is greater than logic (which it frequently violates); and it is greater then rationality (which it considers to be a malleable concept).
There is an old saying [George Chapman] that goes, “Young men think that old men are fools but old men know that young men are fools.”. I consider that to be correct.
I think it is also true and entirely appropriate to paraphrase that comment thus, “Religious people think that atheists are fools but atheists know that the religious are fools.”.