When choosing new Speakers, what matters most to you?

When you buy them what are you going to do with them.  Listen to them.  I therefore suggest you listen to them. Specifications are very unlikely to tell you what they sound like, even if they are an honest and accurate presentation, which many specifications are not.

1. DESIGN. I don't mean that they 'look kool' but rather that they look like they were shaped by an honest sonic objective and that everything...every element defers to that objective. I'm a big fan of Tannoy Legacy and Klipsch Heritage. Timeless design in the broadest sense of the word. Lastly, I need to look at it and it needs to looks interesting.

2. EFFICIENCY + IMPEDANCE. Both together need to be easy. I want more than 91db efficiency and no less than a 4ohm dip. 

3. BIG DRIVERS. I now less prefer small speakers with high excursion and prefer large surfaces producing effortless, velvety bass even at very low volumes.

4. FULL RANGE RESPONSE. I like the simplicity of not having subwoofers. So the LF response needs to reach below 40hz.

5. ADJUSTMENTS FOR HF. I have an 8k notch (loss) in my left ear. My Tannoys allow me to juice the left tweeter a tad to make up for it. This is an amazing feature for someone like me.

I don’t care how it measures if I don’t like the way it sounds. And if I like the way it sounds then why do I care how it measures. It’s not like I have the option to EQ my ears and I doubt they have a flat curve.

The most important spec is price. Why torture or tease yourself with options grossly out of reach? Likewise, you can’t just ignore amplification because if the speakers require different amps then that needs to be in the budget. Reviews and subjective evaluations are much more likely to pique my interest than any measurement can. But they’re also less likely to deter me if I’m already interested. Confirmation bias is human nature. We look for data to support the conclusion that we want.

Bottom line is I’m going to check price and amp compatibility (as relates to price) before anything else, and then look for reviews because I don’t have any experience correlating specs to whether or not a snare hit, cello, or vocal is going to sound right. 

"When auditioning new speakers have you ever listened to a pair you thought you really liked only to realize you didn’t like them at all after seeing their measurements/specifications? "

No! Why on earth would I do that? If they sound good, they sound good, end of story. Sites like ASR look at numbers and not at sounds.

The only thing I don't understand is the type of speaker people listen to. Why on earth would a speaker that sounded great when I was 30, sound worse at 67? That's just it for me, they don't. They still sound great, why keep looking. I know what certain drivers sound like. Even if something is wrong, usually I know how to fix certain kinds of drivers to sound right for me. 

I also know there are cone and voice coil drivers that sound good, but there is always something missing unless I use at least a ring driver/ dome or better yet small push/pull planars or ribbons.. It's the speed that I'm use to and like so much.
I like soft domes in a LS or a single too. A good A/B valve amp don't hurt either. :-)

Regards