As my Masters was on aragonite in NSW caves, please have a look through articles for links to various articles on cave aragonite, including some interesting underwater helictites from some caves on the Nullarbor.

The key point is that calcium carbonate will be precipitated in caves as aragonite, rather than calcite, if there is something else present in solution which prevents calcite from precipitating. A common "something" is the magnesium ion.

Aragonite in caves is usually clear, and sparkling due to its highly reflective crystal facets. Aragonite crystals break across the needles, in contrast to calcite which breaks with a characteristic chamfer.
Aragonite usually forms radiating patterns of crystals, whereas calcite usually forms the more common stalactitic shapes.

Sometimes, needle-form calcite can be confused with aragonite. They are not the same: please see lublinite for more details.