Excellent responses from all.
In your A and B speaker example, I would say, speaker 'B' has better specs, but that doesn't mean it is a better speaker. Though in general, a single cone speaker, unless it is massively expensive, is going to have some problems.
Here is a link to a frequency response graph for a single cone speaker.
Goldwood GW-8003/8 8" Full Range Driver w/Whizzer
http://www.parts-express.com/pdf/290-379g.pdf
Notice how uneven everything gets above 1khz. This is typical. Now the speaker in the link above is only US$25, so we can't expect miracles.
However, here is a link to a single Dayton 4" single cone full range speaker that has been equalized with a graphic equalizer to produce amazing response.
HTGuide Forum - " Full Range " Dayton RS100S project
Compare the two graphs in post#1 with the graph the link at the top.
As pointed out, the frequency response rating is either -3db or -6db down from the average level. Three db is a slight but noticeable change in the sound level, but it represents a doubling or halving of the power levels.
But the tuning of the speaker cabinet has a great deal to do with how you perceive the bass level. You can tune a cabinet to have a slight peak in the bass, but that means, below the peak, it drops off at a faster rate. If this cabinet tuning get too extreme, you have a cabinet with what is called 'one note bass'; in other words, a typical 'boom' box.
Using this cabinet tuning technique, you can make a speaker that has poor low end response sound like it has good bass. So, the Speaker 'A', could sound good, yet still have a seemingly poor 80hz cutoff on the low end.
As to Sensitivity, initially, upon its inception, it seemed like a good idea since it provided a way to compare all speaker with the same input. Typically it is measured with a calibrated microphone and an Sound Pressure Level (SPL) meter at a specific level at a specific distance.
But a controversy occurred. Should speaker all be fed the exact same signal, 2.83 volts, or should the be fed the same power (1 watt). Speaker are actually voltage driven devices. You feed them a voltage signal and they consume power. So, that school of thought says the fair way to compare speakers is with a fix and known (2.83v) signal.
Other say if you feed 1 watt to an 8 ohm speaker, then you should feed 1 watt to a 4 ohm speaker. But the voltage necessary to feed one watt to a 4 ohms speaker is 2 volts, and the voltage necessary to feed one watt to 16 ohms is 4 volts. To get these voltages, you are either turning the volume control up or down to reach one watt. But how can you say you compared two speakers equally when you turned the volume up or down for one of them?
So, frequently if you look at full specs, it with either say, 90db at 2.83v measured at 1 meter. Or it will say, 90db at 1 watt measured at 1 meter. Unless the speakers are both 8 ohms, that's not necessarily a fair comparison.
Most have adopted a uniform 2.83 volts, others choose which ever method gives them the better numbers.
The crossover frequencies are nice information to have and give you some sense of the underlying design philosophy, but you can't really make a value judgment based on that information. Again, it is just nice to know information.
So, I guess when you add it all up, even though there seem to be standards for these various rating, they are not all that standardized. For example, if you want to inflate your frequency response, that is, make it seem lower and higher than it really is, you simply quote it at -6db instead of -3db. Typically that will gain you roughly 5hz or possibly a little more on the low end.
If you want higher apparent Sensitivity, you test it at both a fixed 2.82volts and a 1 watt and use which ever number is higher.
Remember from above, that 3db represents twice as much power. So, if you have two speakers, and one is rated at 90db and the other is rated at 87db, the 90db speaker is going to take half the power to reach a given volume.
But also remember that power and volume aren't linear. It takes 10 TIMES the power to double the volume, and a slight but noticeable change in volume represents a doubling of the power. So, in the example, even though it takes twice the power for one speaker to equal the perceived sound level of the other, that is only a slight difference in perceived volume level.
So, the conclusion is that you can't rely totally on specs. They do give you valuable information, but nothing tells you more than a good long listen to the speaker using material you are familiar with.
So in summary -
Frequency response is the working range of the speaker. But the sound doesn't absolutely cut off at those frequencies. At those rated frequencies, the sound has started to roll off or fade, and continues to fade on a shallow downward slope. You do get sound below these rated level, it is just reduced sound. So, even a speaker rated at 40hz might still allow you to hear 30hz noted, they just won't be very loud.
Sensitivity is a supposedly standardized method of indicating a speakers efficiency. The higher the number the more efficient the speaker is. Most speaker are in the range of 85db to 95db, with most being in the high 80's and a few in the low 90's. This is mostly a concern if you are using a low powered amp. But it does give some way of making a relative judgment on a speaker.
Crossovers are neither good or bad. If you have a speaker with more than one driver, it must have a crossover of some type. The specific frequencies can give you some underlying sense of the design, but there is nothing you can do about them. The selected frequencies have been matched to the specific speakers, and must be where they are.
Another aspects of a speaker, is whether it is ported or sealed. Ported speakers are generally more efficient, but that doesn't mean sealed speaker sound worse. A seal speaker or acoustic suspension or infinite baffle speaker and better control cone movement, and in better speakers, can actually sound better.
Ported cabinets or Bass Reflex cabinets have an extra hole or opening cut into them which is tuned by a tube or port to a specific frequency; usually a very low frequency. This raise the overall efficiency of the speaker and cause it to resonate at a predetermined low frequency that help re-enforce the bass.
Either cabinet design done wrong will sound bad, but, if done right, either type can sound very good.
Ported cabinets come in various type. They can be front ported, rear ported, and technically the port can be on the bottom, the top, or the sides, it really doesn't matter.
Rear ports are more common now, but it is mostly a trend. The problem with rear ports is they require a certain amount of distance between the speaker and the wall behind. Many living rooms are too small to accommodate this distance. Though, fairly, the distance is only significant for larger speakers.
Just a few additional thoughts.
Steve/bluewizard