Okay, they can both be great, or suck, depending on how well they are done, and what parts are used. There is not one speaker system in the world that is not a compromise. None. You are compromising something with any design you choose, regardless of what it costs.
Since the 2-ways are getting "picked on" at the moment, if you'd like, I could tear a hole a mile wide, in the 3-way design, by pointing out the plethora of problems with them. I can also do the same with my single-driver system, 2-way, 4-way, subs and sats, and so on.
The bottom line that I've gotten out of the numerous threads regarding speakers on this forum, is that different people like different strengths and can accept different weaknesses in speakers.
It breaks down into 2 main categories, bass lovers, and those who can live with less bass, although not much less. A bass lover will accept what the added driver and crossover complexity will do to the sound, to get his level of deep bass response. One who will accept less bass will do that to get the coherence he wants out of his 2-way, or 1-way.
Oh, I can already hear it. "What do you mean that my 3-way isn't coherent?!". It may be. But likely not as coherent as a less complex speaker design. In a cost no object speaker, maybe the 3 way will be as coherent, but there will be alot of money involved. Not everyone has that amount of money. Excellent bass response is expensive. Probably the most expensive and difficult thing to get in a speaker design. So many would choose to accept a 40-50Hz bottom end, and save a large amount of money, and get a more coherent sound for the money that they can spend.
The woofers are the most expensive driver generally. They also require a large box size and bracing for lower bass. This translates into money. Added crossover costs more. Added design complexity costs more. For a given price, say about $4k, you can get better quality parts and design for your money in a 2-way, if you can live with higher than 20Hz bottom end. To get the same quality in a 3-way with deep bass response, you are going to about double the cost to $8k. And you still may lose something in the bargain, because added complexity means more likelihood of error, or problems.
There are some things, like deep bass response that most 2-way, and 1-way speakers will never do as good as a quality 3-way, but folks, and I know you hate to hear this, there are some things that a 1-way or 2-way speaker will do, that a 3-way never will do as well. Like point-source imaging. Lack of driver overlap, and no(1-way) or less(2-way)crossover distortion. You may think that your 3-way is perfect, but that is not right. It has problems in those areas no matter how good it is.
So what I'm saying is, buy what you like. You are the one who has to listen to it. Convincing us that a certain type of speaker is better than another is chasing your tail. In truth, you are only exhanging one set of problems for another. The problems that bother you the least, and the strengths that you require the most, will be your kind of speaker, no matter what I, or anyone else will say.