* Can you cook with it? Some of these products are damaged by heat; others are not. A personal observation: Putting them into hot coffee seems to have minimal effect on sweetening ability.
* Taste and/or aftertaste: some products leave a very distinctive aftertaste.
* Bad press. Aspartame in particular was hit with a ton of negative claims implying it was dangerous, but remember that these products have been approved by the U.S. Food and Drug Administration.
* Cost. The newer sweeteners that maintain patent protection also are the most costly.
* Availability. If you're at a restaurant, and there's white, blue, and pink stuff available, that might be all that they have. But ask: several times, I've found that the restaurant does have the yellow stuff but only produces it upon request.

You'll have to decide which criteria are important to you. And if nothing else comes to mind, you can always choose your sweetener based on the color of the packet.