What type of speaker would sound better?

@gdaddy1 

+1 I have used your automotive manufacturing analogy many times to debunk the need for a Speaker to cost $100K+ (or $50K for that matter!!). Speakers just aren’t that complex and science on good sound is pretty much decided outside of driver technology and exotic cabinet materials. None of which cost anywhere near as much to design and manufacture as an automobile, even a crappy car! 
 

To the OP’s question, do a deep dive into either the 2 way or the 3 way and see how the thing is built. What separates a good speaker from a great speaker is the driver technology (think ScanSpeak, SB Acoustics Satori, Purifi), and cabinet construction. Cabinet bracing is SOOOO important and the brands that cheap out on it are putting one over on you (Klipsch, Tekton, Zu Audio, etc.). People like to talk down about B&W and Wilson because the voicing is a little hot, but their cabinet technology and drives are top notch! If the 2 way has better drivers and cabinet than the 3 way, it has a strong chance of sounding better. 

Sadly or maybe not so sadly, there is no magic formula for what is going to sound best. The room itself, its size and shape, listening position, acoustic treatments, type of music and whether or not you intend to augment low frequency response with subwoofers or not all play into what will work the best for you. In general, the larger the room the more low frequency cone area you need to have for full bandwidth response. The louder you want to listen, the more low frequency cone area you want in general. In your room I would want something with a couple of 12" drivers for low frequency support so that almost certainly means at least a 3 way system if not 4 way. A pair of Legacy Focus SE for mains would likely work very well in your room. Not cheap but this is a full bandwidth solution with a very healthy dynamic range and by some reviewers among the very best available at any price. Worthy contender at the very least. 

There is also the one driver option.  Can be magical when done correctly!

I agree with @knotscott, my speakers are two way, no hole in the middle and they have low bass. 

Mike

You say lower quality vs higher quality and that’s a very subjective decision to make. You should get an idea what matters to you. Personally I would always go on the quality side, but I haven’t experienced much hearing degradation and understand what I like. If those circumstanced changed, it’s always nice to have the full range speaker if it fits the room better.

Another thought is that sometimes a great 2 way and a high quality pair of subs betters a 3 way speaker. It’s hard to get good bass in a speaker for under 15k at least.

Gaddy, I appreciate your opinion and agree with it, however when a manufacturer that has hundreds of thousands of employees and an incredible economy of scale significantly drives down the cost over time- 94 million cars made each year. A car door might cost $20 after the first 5 million. Still, I'm generally in agreement with your point.