With speakers the whole balanced/unbalanced thing isn't there. Speakers are carrying a much higher wattage. The Eliminators in question here are PA speakers. They will take a standard TS connection on a speaker cable. Often speaker cables will use a larger fatter 1/4" connector since the cable will be a higher gauge and often won't fit in one of the smaller 1/4" connector sleeves. There is no real sound difference between a speaker cable with a 1/4" tip or one with a Neutrik NL4 connector (commonly referred to as speakon).
The real advantage of a speker cable with NL4 connectors is in the logistics. 1/4" cables are friction based, and often the jacks may not be too tight which makes them easier to accidentally unplug. Neutrik does make a locking 1/4" jack that can really help this out. Another problem is that when a 1/4" cable comes unplugged you are leaving both leads of the cable exposed. If the amp is sending signal, then the load has nowhere to go and technically the cable is still hot, but with exposed leads (tip and sleeve). Repluggng a 1/4" speaker cable that is hot will often make a pop in the system. Physically as you plug it in, the tip makes contact with the pole on the jack that is expecting to see the sleeve, and then slides through till it finally gets to the part of the jack that is expecting the tip. This can cause crackles and pops as it does this, and adds unnecessary stress to your drivers and even the internal crossover on your speaker. In general this isn't normally damaging to the speaker in real life, but the principle is there and there is always the added possibility of damaging something.
One other thing is that 1/4" cables are most often soldered at their leads. This means that when a cable is pulled or tugged, you are applying pressure to the solder. In real life it means it will be slower to repair, and yiou have to have a soldering iron with you to make the repair. If the positive lead were to come free, it could easily "float" inside the connector and make contact with the negative lead which is bad on both your speaker and your amp. NL4 plugs are connected internally by set screws or small phillips head screws. The connections are physically seperated inside the connector and there is a strain relief system in place. The connectors are pretty durable and have a twist lock mechanism in them so they stay seated when plugged in. NL4 also connects all poles evenly when plugging them into a speaker cabinet which is noise free when hot plugging a cable. In addition, NL4 is capable of running 4 wires through it's connector so 1 cable can carry a biamped signal if set up properly. Neutrik also makes an NL8 connector that carries 8 wires inside it for a single cable run in a 4 way system, 2 biamped, etc... NL4 connectors are pretty durable, cost effective, stable, and easy to repair. This is one good reason why so many people use them in the pro audio world.
NL4 and NL8 connectors can also be used on power cords. This seems to be gaining in popularity as it is typically a more secure and more affordable solution with certain power runs. If you think about it, do you really want an IEC style power cord sticking out of the back of your powered line array? If that cord slips free you have to lower the array just to plug it in. With NL4 and NL8 it locks into place
