Your questions do not have simple answers that will be true in all cases. This is because whether a particular 2-way speaker sounds better or worse than a particular 3-way speaker depends on what speakers we are talking about, as well as what qualities matter to an individual (as one speaker may sound better with some aspects of the sound, and another may sound better with others).
In other words, some 2-way bookshelf speakers will sound better in soundstage and imaging and dialog than some 3-way speakers, and some 3-way speakers will sound better in soundstage and imaging and dialog than some 2-way speakers. To put this another way, whether a speaker is good or not is not determined by whether it is 2-way or 3-way.
If we are looking at a particular price point, one can have more expensive drivers if there are fewer of them, and also the crossover is simplified by having fewer divisions of frequencies (and consequently will be cheaper to make, if all else is equal), and so there will be more money for better parts in the crossover, or that money can be put into more expensive drivers or a better cabinet or whatever. Plus, the smaller the speaker overall, the cheaper it is to ship (though if the speakers get too small, it will be a problem for them going deep enough to mate well with a subwoofer; the laws of physics cannot be violated). If one is buying a speaker in an ordinary retail store, the cost of shipping from the factory to the store is part of the retail price that you are going to have to pay. And so again, at a particular price point, that savings in shipping could be going into better drivers in the relatively small two-way speaker.
One of the mistakes that many people make in their comparisons is to compare models in a particular line of speakers. That is a mistake because the bookshelf speakers in that line are cheaper, so that what one is doing is comparing relatively cheap speakers with more expensive speakers. Being more expensive, the more expensive speakers
ought to be better in some way. But if we are talking about a particular price point, the bookshelf speakers that will cost the same as a tower speaker will be in a higher line of speakers, and those are what should be compared. Unless, of course, one is taking the approach of having a better subwoofer instead, in which case one's listening comparisons should be done with the subwoofers properly set up, not with the speakers playing full range. So that is another way that people do not properly compare, as, of course, in the same line, generally the tower speaker will go deeper in the bass, but that is not important if one is going to be using a subwoofer in one's system to handle that deep bass anyway.
If we are talking about a system where one will use a subwoofer for the very deepest bass, essentially if the other speakers are two-way, the overall system will be three way (as the frequencies are divided into three parts, with the tweeter getting the treble, the woofer in the two-way speaker getting the midbass, and the subwoofer getting the deep bass), and if the other speakers are three-way, the overall system will be four-way with a subwoofer taking care of the deepest bass. In cases with a subwoofer, the main channel speakers are not being required to do the full range of frequencies (or at least need not be).
The long and the short of it, in my opinion, is this: Do not buy based upon whether it is two-way or three-way or four-way or whatever-way; buy based on actual performance, and on aspects of the performance that will actually matter in the use to which one will put the speaker (by that second point I mean things like, do not worry about the deepest bass of a speaker if you are going to actually be using a subwoofer for those frequencies anyway).
In my particular case, I use two-way bookshelf speakers for all channels. But I did not buy them because they were two-way; if I had found a better speaker that would suit my needs (which obviously includes price) that happened to be three-way or four-way, I would not have hesitated to go with them instead.
In my particular case, going higher up in the line (at the time I bought
mine [the ones at the link are slightly different with an altered crossover, but otherwise the same]) would have involved using the same tweeter and midbass driver, and with
the cheapest tower, it added a second midbass driver, and with
the more expensive tower, it added a larger woofer instead of a second midbass driver. (At the time I bought mine, those were the three models available; since then new models have appeared.) In other words, these three speakers used the same tweeter, basically the same midbass driver (though in the bookshelf speakers it was slightly modified, with a smaller dustcap), and then whether there was another driver or not, and what it was if there was one, is what distinguished the models. They also had different crossovers, which can seriously affect the sound, particularly if one of them is poorly made. Well, the cheapest of these is a bookshelf speaker that has a -3dB point of 50Hz, which is low enough to mate well with a subwoofer, which is how I was going to use them. Neither of the towers would fit below my TV, so I would either be using a bookshelf speaker or I would be using
the center channel speaker, which again uses the same tweeter and uses two of basically the same midbass drivers. It would be an excellent match, of course, for the others, but not a
perfect match, because it is a different speaker. Now, the prices went up fast, and buying one pair of the best towers (versus one pair of the bookshelf speakers) would have taken up the money I spent on my subwoofers (I bought my subwoofers used at a great price), and would not give me nearly as deep bass for that money. (If I had purchased my subwoofers new, that price difference would have paid for one of them, which still would give me much deeper bass, for that same price.)
So, what have I given up? Well, the tower speakers (especially the best ones), if used without a subwoofer, would be able to give me significantly deeper bass. Since I don't actually use them that way in my home theater system, that does not matter. I also am giving up maximum SPL, as the towers will play louder, due to moving up the crossover frequency to the tweeter, and having an additional woofer deal with the deepest bass. However, my system will play loud and clear at levels I find painful, so that does not matter in my case either.
In my case, with my use, I think I made the right decision. However, different people have different things that they are wanting, and are also dealing with different price points, and so their decisions may be quite different from mine, without either of us being wrong to decide what we decide. (Of course, either or both of us could be wrong to decide what we decide, but that is always a possibility, whether we make the same choice or not.)
Edited to add:
Here is a view of a brochure with all of the then-available models:
http://www.kellsieavdesign.com/AC_brochure002.JPG
Please note, the frequency responses listed in it, if they do not specify a tolerance (e.g., +/-3dB), they are specifying with the bass at -6dB. Thus, the Leisure 2SE (original U.S. version) is -3dB @ 50Hz, and at -6dB @ 42 Hz mentioned in the brochure.
Also, most of the speakers sold on eBay are not the U.S. version, but are an inferior version. There used to be 4 versions, but there now appear to be even more, with some of them now not only using a cheaper woofer, but also using a cheaper tweeter as well (not to mention the differences in crossover and bass port).
Here you can see some pictures of differences between the U.S. version and a cheaper "international" version:
http://www.kellsieavdesign.com/products/US_vs_CH.htm
The U.S. version has a smaller, flared port on the back, and the international uses a larger, straight port, resulting in less flat response in the bass (with a hump in the upper bass) and down -3dB at 55Hz instead of 50Hz, though with some of the newer versions with lesser woofers, it might now be worse with new purchases of international versions.
The U.S. version has a higher quality finish.
The U.S. version has no red Chinese lettering on the back plate.
The U.S. version has on the back plate "Kellsie Audio & Video Designs," who at the time were not only the only authorized U.S. importer, but actually were involved in redesigning the speakers to improve them (as mentioned above).
