They are two different minerals with different properties.
Sapphire is a Corundum which really is aluminium oxide. Tourmalines are trigonal borosilicates of the cyclosilicate superclass.
I'll cut through the science and just explain this to you as if you were choosing one or the other as a piece of jewelry. (I hope that's what you were looking for!)
Sapphires are harder and less brittle, and therefore the more durable of the two. Even so, Tourmaline is not considered a fragile stone and can withstand reasonable abuse. Both stone make great jewelry stones!
Both stones are pleochroic, which means that they can show different colors in different directions. Of the two, Tourmaline has stronger pleochroism. If you observe a Pink Tourmaline carefully, you may see some orange or purple flashes. This is less obvious in Sapphire.
To the trained eye, Pink Sapphires and Pink Tourmalines may have slight nuances in hue that can help differentiate one stone from the other. A trained eye can also differentiate the two based on inclusions. For instance, Tourmalines often have liquid-like channels called Trichites, color zoning in a triangular or Y-shape and also exhibit a doubling of facets due to the way light refracts in the crystal. Sapphires often have small crystals and needle-like inclusions.
Prices of Pink Sapphires are generally higher than Pink Tourmalines. For wholesale prices of stones in the USA, check "The Guide". "The Guide" publishes wholesale gemstone prices in the US which you can subscribe to at US$195 a year. Their website is www.gemguide.com
I LOVE gemstones and am a gemologist.