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What's the difference between Lambert conformal conic projection and Lambert conformal conic alternative projection in PROJ4?

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According to the discussion at http://osgeo-org.1560.x6.nabble.com/Re-Grown-error-if-re-projecting-from-4269-to-LCC-2285-and-backward-multiple-times-td5340627.html

LCC has an iteration loop criterion (in the inverse) of 1e-10, whereas LCCA is somewhat more accurate with 1e-12. Furthermore LCCA works with a Newton iteration scheme. This could be faster than iteration by successive approximation, but there are a couple of minor inefficiencies in the code, like function calls instead of inline, but YMMV.

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