It seems to me that "leading edge" is the more established phrase, while "bleeding edge" is basically the same thing but the user has adapted the phrase for extra (rather meaningless) emphasis.
Or is there a meaningful distinction between the two?
There is, in fact, a distinction.
Leading edge in this sense, means cutting edge. It refers to the most highly sophisticated development in a field. However, it rarely or never has the connotation of risky or untested. It is almost always used to describe the best; not necessarily the newest.
Bleeding edge would refer to a development that is so new that it could have a high risk of being unreliable and may incur greater expense in order to use it:
There is a slight semantic difference here.
Leading edge refers to people or things who are the foremost or the best in a technology, science, art, skill, etc.
Bleeding edge also refers to this fact of being in the foremost, but the difference between bleeding edge and leading edge, is that bleeding edge is risky. Leading edge is not risky. Bleeding edge is. For example:
PC Encyclopedia defines bleeding edge:
Note how it's derived from leading edge.
Leading edge is a term for being in the forefront of a field. The term probably comes from the leading edge of an airfoil or similar body in aerodynamics. Bleeding edge is a play on leading edge, referring to the high risk of leading edge technology failing or encountering problems.