Co-axial vs Components
What's the difference?
Co-axials are speakers that have the tweeter permanently mounted in the middle of the midwoofer. Co-axials typically do not have external passive crossovers.....only a capacitor in-line with the tweeter to highpass the tweeter. They are generally much cheaper than components, and will work well off of headunit power (but will perform well off of external amplification aswell).
Components have separate midwoofers and tweeters as well as an external passive crossover. The midwoofers and tweeters are separated for a number of reasons.....for example, to allow optimal speaker placement. The passive crossovers are usually quite complex (for more advanced than what's used for co-axials) and are designed to optimize the performance of the speakers (by way of crossover points, crossover slopes, tweeter attenuation, tweeter protection, impedence compensation [zobel network], etc etc). The speakers used in component sets are typically of much higher quality and better performance that those used in co-axials. Typically components are best used with external amplification only.
2-Way vs. 3-Way
In a perfect world, we'd have a single speaker that could reproduce all frequencies perfectly, 20hz to 20khz. Unfortunately for us, such speaker does not exist…..so, we need to break the frequency spectrum down and play it through multiple speakers (mids, tweeters, subs, etc). This is where we get "2-ways, 3-ways, 5-ways, etc" from.
In co-axials, a 2-way speaker is a speaker that contains only a midwoofer and a tweeter…..the midwoofer playing the lower frequencies (down to around 80hz or so), the tweeter playing the higher frequencies (around 3khz or 4khz and up). 3-way co-axials typically have a midwoofer, tweeter and "supertweeter", with the supertweeter being designated to handle the very, very high frequencies only. Co-axials can go as high as 5-way (midwoofer, midrange, smaller midrange, tweeter and supertweeter). For all intents and purposes, anything more than 2-way in co-axials is a marketing gimmick. Going with 3-way co-axials or higher usually does not increase performance much, if at all.
For component speakers, a 3-way system includes a dedicated midbass (generally plays around 60hz-350hz), a dedicated midrange (generally plays around 350hz-6500hz or so), and a tweeter (generally 6500hz and up). Whereas a 2-way system is only a midwoofer (playing around 60hz-4000hz or so) and a tweeter (4000hz and up). Ideally, for a 3-way system, you'd want to put the midbass in your door, and have kicks built for the midrange & tweeter. For a 2-way component set, kickpanels or door mounting will suffice with generally good results.
General advantages of a 3-way component set:
1) There isn't a crossover point in the middle of the midrange frequencies (which are generally the most important to imaging and tonality), and they aren't being split up between drivers like they sometimes are in a 2-way setup. In a 3-way, they will be played by mainly one speaker, which is the dedicated midrange.
2) In a lot of cars, the mids will need to be flipped out of phase to help correct some midrange frequency phasing problems. In a 2-way system where one speaker plays midrange & midbass, running one of them out of phase will decrease the midbass impact. By running a 3-way, the midrange can be flipped out of phase and it has no effect on the midbass since it is being played by a separate driver.
3) The midrange and midbass frequencies in a 3-way may sound "cleaner" since each speaker has more of a limited bandwidth to play.
Disadvantages of a 3-way component set:
1) Tuning and aiming the speakers can be a much bigger pain the ass with 3-ways. Installation, tuning, phasing and aiming speakers will be much easier/quicker to perfect with 2-ways.
2) Room. It can be much more difficult find the room to fit all of the speakers. In some cars, kickpanels are simply out of the question.
3) Money. 3-ways are normally considerably more expensive than 2-ways.
As you can see, 3-ways aren't necessarily better than 2-way. It's more of a personal preference. Some ppl would rather have a 3-way (for the advantages above), some ppl would rather have a 2-way (easier to tune, less room is occupied, etc).