The spell parser should almost always be more accurate. The parser uses actual formulas and such, I have no idea what the wiki does.
That said, there may be some discrepancies due to things like level adjustments, base calcs, etc. It's hard to make either one completely accurate because there are runtime things that cannot be reflected easily in a static display like the parser or wiki. As a general rule though, I would tend to trust the parser a bit more.