x > y yields True if x is determined to be greater than y.
> > yields True if the form a strictly decreasing sequence.
Greater gives True or False when its arguments are real numbers.
Greater does some simplification when its arguments are not numbers.
For exact numeric quantities, Greater internally uses numerical approximations to establish numerical ordering. This process can be affected by the setting of the global variable $MaxExtraPrecision.
See The Mathematica Book: Section 1.5.6.
See also: GreaterEqual, Less, Positive, Element.