two way v. three way speakers


I recently heard some magico mini's at a friend's house. They sounded amazing. And they were 'only' a two way speakers, but they filled the room with amazing sound. So now I wonder, what does the additional driver add, especially when it is the same size as the second driver. For example, the SF Olympica III's have two drivers of the same size. I know that third driver adds a lot to the price, but what does it sonically? Thank you all in advance.
elegal
All things being equal a three way is better than a two way, due the three way not sharing mid/bass range in a single driver. But this not the end of the story, driver selection, crossover design/integration and cabinet construction also are important in overall sound quality. And as mentioned by MceLjo, amp choice is also very important, why have great speakers if they are under driven by the amp?
@Maxboy00 - Because you can't afford both! Obviously, there has to be some balance, but I like knowing that my speakers are limited by the rest of my system than the other way around. Just my budget compromise preference.
These days there are some brands who can really make good crossovers. In the past there were many 4 or 4 way speakers which did not sound that great. Caused by the weak crossovers.

When you compare the 2 and 3 way togheter. The mid freq are often more open, warmer and more focussed with the 3 way. In the past many 2 way loudspeakers had a much better sharpness in focus. These days that does not count anymore.

I also prefer speakers who have 2 units for there low freq. It is faster than one big unit. When every speaker has his own freq. response the authority is bigger. There is a lot more control.
@McelJO, Yes balance and budget constraints are always a point of compromise in any system, but I was agreeing with you about the use of a quality amp to get better performance from a good pair of speakers.