When you ask - what is the difference between a good audio system and a bad audio system?? To me, it means a few important things:
1. Quality of speaker. This is the most important component as it is the one that literally produces the sound we hear. A speaker generally produces good sound when it has a stiff and strong cabinet that does not vibrate when the drivers (cones) move up and down to produce sound. This is usually achieved with a cabinet made out of wood instead of cheap thin plastic, thicker wood walls instead of thin walls that can vibrate, internal cross bracing to make the cabinet stiffer, etc. This usually results in a cabinet that is much heavier.
So, first thumb rule of speaker is - the heavier it is, the better. Also, if you knock on it with your knuckles, it should sound "dead" or filled up, and should not sound hollow or like a drum (which indicates it vibrates more). In this sense, a speaker design is the exact opposite of a musical instrument. A musical instrument is specifically designed to vibrate, while a speaker cabinet is designed to vibrate as little as possible.
Frequency range of a speaker indicates how low it will go (ignore the higher number). If you really like your bass, then go for a speaker that goes down to 40-50Hz. Most floorstanders will do this. If you have bookshelf speakers, and if you like a lot of bass, you will need a sub-woofer. This is further complicated by your speaker positioning. Keeping the speaker closer to the wall (most people tend to do) actually results in more bass as the bass gets reflected by the walls, but unfortunately, it also results in very boomy bass - so you are sacrificing quantity for quality. Ideally, you want to place your speakers 2 ft away from your walls (or less if your speaker has the port hole in the front instead of the rear).
Sensitivity indicates how loud your speaker will play for the same amplification. A 90-92db speaker will play a great deal louder than a 85db speaker as db is a log scale which means that the volume starts doubling even for small increases. This means that a 92db speaker can be easily driven by a lower power amp.
Impedance of speaker indicates how much current or power it pulls from the amp. Most speakers are 8 ohms, but a 4 ohm speaker will pull double the power from your amp than your 8 ohm speaker. Most AVRs do not even support 4 ohm speakers properly as their power supply is not strong enough. This is further complicated by the fact that the impedance actually varies depending on the frequency of sound your speaker is trying to play. So a "6 ohm nominal" speaker such as yours will most likely be dipping down to 4 ohms in certain frequencies. This means that in complex music pieces, it is really stretching your amp to its limits, and also why you feel sometimes that certain things sound worse than the other.
General thumb rule is that people like to go for overkill when it comes to the amp. Also why you will very often notice a signficant improvement in quality if you switch from your AVR to a stereo amp or multichannel power amp that legitimately supports 4ohm speakers for extended periods of time and also have significantly better quality power supplies.
2. Amplifier - Although you only asked for speakers, it is a speaker-amp combination that makes for a complete discussion. Like i said, the most aspect of an amp is the quality of its power supply. Typically, this means a toroid transformer (which is heavy). So same crude funda applies here. The heavier the amp, the better it is, usually. For both speakers and amps, you should struggle to lift them - this is as crude as it gets but it actually works a great deal of the time!
In terms of specs, look for an amp that supports 4 ohm speakers. Another thumb rule is - the amp should be able to deliver close to double the power in 4 ohms than it does in 8 ohms. So, an amp that delivers 100W RMS for 8ohm speakers (all channel driven, not just 2 channels driven as AVRs like to sneakily do) - should deliver 200W of power for a 4 ohm speaker - in all channels simultaneously. This indicates a really well built power supply that can "scale up" the power as needed by the speaker. This is often wishful thinking unless you buy a power amp. So compromise - even if your amp delivers 150W for 4 ohm speakers, consider that to be a "good deal" for entry to mid level setups.
If an AVR or amp does not even bother to display 4 ohm specs in their spec sheet, it usually means they do not support 4 ohm speakers at all. Which also includes your 6 ohm speakers - most impedance curves I have seen for 6 ohm speakers actually routinely go down to 4 ohms in certain frequencies.
