Friction shifting allows the derailleur an infinite number of positions to be in. It is, at times, depending on your level of riding expertise, necessary to "trim" your shift a wee bit more or less to find the sweet spot. Indexed shifting requires that you pull the shift lever enough for it to click. If properly adjusted, that click will accurately position the drive chain on the correct cog (rear wheel) with no need to fuss around to get it perfect.

For my money, I definitely prefer indexed shifting. The new shifter design, called Brifters (Brake + RIFTERS = Brifters) are indexed shifting components and my absolute riding preference.