Like others have already said, its ultimately up to what you think sounds best. Generally the more expensive speakers will sound better, but not all the time. I know you're looking for X is better than Y when it comes to speakers, but that isn't always the case. However, there are some things which make a definite difference though. The materials used can have a dramatic impact on the sound.
For the woofer, there are lots of materials used. You want to look for materials that are rigid and will not flex as much. Distortion occurs when the cone flexes. Woofer cones are made out of everything from everyday materials like paper and aluminum to more complicated things like polypropylene and kevlar. Here's
a list of nearly all the materials used to build speakers. But remember, its whatever sounds best to you.
You'll likely end up with tweeters made of either silk or metal (aluminum, titanium, etc). Either one is great as a material. Some people love one and hate the other, while others don't have a preference.
While you're researching online, keep in mind that some of high-end brands have similar specs (i.e. frequency, wattage, responsiveness, etc.) as some of the low-end brands. So don't just go online and look for good specs and a low price. For instance, the best set of component speakers I've heard were made by Hertz. The Hertz HSK165 components have a slightly narrower frequency range than the Sony XS-GTX1622S components. I don't know an exact price for the Hertz, but they're probably in the $500-$600 range and could be more. Whereas the Sonys will set you back $120. The Hertz speakers will likely sound much better to you even with a slightly narrower frequency range. That's why listening to speakers is so important.
I always tell people to just go to several local car audio stores and skip looking at speakers online. This will give you a better idea of which brands your ears like better. Speaker manufacturers tend to have a similar sound from their speakers, but not always. So if you like a set of Alpines, for instance, don't assume that you'll like every Alpine speaker.
You'll probably want to do a bit of online research to make sure the speakers you're thinking of buying have good reviews from other people. You don't want to end up with speakers that are known to give out after a year. From there you can narrow it down to perhaps 2 or 3 sets of speakers. Then go back to the store to listen again and then buy your favorite.
When you go to the stores, make sure to take your iPod or some CDs so you can demo music that you're already familiar with. That way you aren't forced to listen to the radio or whatever Top 40 song the store has on hand.
Good luck with finding some speakers and keep us updated when you buy them!