In general, lipsticks with names such as Cinnamon Spice have a warm undertone, while those labeled something like Icy Pink have a cool cast. People with a peach or orange essence to their skin are considered to be warm-toned, while those with a blue or pink undertone are said to be cool-toned. Chances are, you'll be instinctively attracted to the right lipstick color family for you, as cool-toned people tend to prefer the clear, icy shades while those with warmer skin tones usually pick the tawny, spicy hues. Corals or dusty pinks, brick reds and bronzed plums tend to suit those with warmer skin tones, while clear pinks, reds and plums tend to suit those with cooler skin tones. Comparing skin colors and lipstick shade preferences with friends can help you better understand the principles of cool and warm tones, too. The best lipstick colors tend to make a person's face look less lined and shadowed. If you appear to look better in certain lipsticks than others, chances are they are in the ideal tones for your skin.
Make Up For Ever has a "Lipstick Finder" tool which helps you choose lipstick shades that coordinate with your skin tone. You just start out by selecting your skin tone and the Lipstick Finder will walk you through to your perfect shade(s). You can access it here: http://www.sephora.com/browse/brand_hierarchy.jhtm
I know this doesn't really address your question specifically about pink lipsticks, but hopefully some of this info will help.
pink is basically light red, right? add a little yellow or orange and it goes warm... add a little blue or violet it goes cool... if you tend to like "earthy" tones, that will probably have warm pinks. red lipstick is a lot like this too. took me FOREVER to find the right "warm red" but it made all the difference in the world. a red with too much blue/violet in it just looks wrong with my skin tone.
A warm pink tends to have a peachier base, and a cooler pink will be blue-based.
If your complexion is neutral, you can probably wear either. If your skin is cooler (you have pink undertones all over, not just in your face), you will likely look better in cool pinks; if your skin is warmer (i.e. a yellow undertone, you tan in the sun without sun protection, etc.), then you may look best in warmer pinks.
. . . and if you're not sure about your skin's undertone, you can hold up your inner wrist against a piece of truly white paper, in natural daylight, and check to see whether your skin looks more peachy/yellow or blue/pink. (Ignore any sallowness or tanning--you're looking for the undertone, which never changes.)