As near as I can tell:
The near implies closeness, a familiarity with the subject matter. You are narrowly focused on the object of conjecture, and applying your specialized experience to test it.
As far as I can tell:
You turn your eyes to the far reaching implications of a hypothesis. Scanning the horizon for other possibilities, you compare the obvious suspects to see which is mostly likely to be correct.
The amazing thing happens when you combine the two. Now you have the full context needed to see problems (and countermeasures) more clearly. Try it the next time you're stuck challenging the status quo.
Bonus: here's Kim B's post on the conversation - Comparative Context