The X2 is a digital system that converts your signal into a digital transmission, thus avoiding the analog dynamic (companding) and bandwidth (no low end) limits of older sytems. The technology for MI use was invented by a company called X-Wire, who were subsequently bought out by Sennheiser. Sennheiser marketed their own version of the X-Wire and called it the D-100 and D-1000. I've had several of the D-1000's in various applications, and they've always been stellar, but Sennheiser priced them too high and they never sold well. ( I bought all mine used). Sennheiser sold off the X-Wire rights and now you have "X2" or
X-Wire version 2.0 which, IIRC, is owned by Line 6.
The reason wireless units specify alkaline instead of rechargable batteries is twofold: alkaline batteries are higher in voltage for a given size. A "9 volt" alkaline battery is actually 9 volts, but in a rechargable form, it is only 7.2 or 8.4 volts. The other is that with NiCad batteries, in addition to having lower voltage, they also have lower current output, rated in mAh (milliampere-hours ) and thus, an extremely short duty cycle. Additionally, they will also develop a 'memory' over time and recharge less and less with each use.
New NiMH batteries are a different story provided that you know which ones to buy. They still have a lower voltage rating but can have much higher current capacity than an alkaline equivalent, so Ohm's Law dictates that if a certain amount of power is required to operate a wireless unit and the voltage is lower, the current output will have be higher in order to provide the same amount of power. Alkaline "AA" size batteries have a 1250 mAh rating under load, but I have seen "AA" NiMH batteries with ratings as high as 2900 mAh. I found a link to a wiki page that comparison lists the different types of consumer batteries,
http://en.wikipedia.org/wiki/List_of_battery_sizes but the caveat I will add is that while alkaline ratings may seem inordinately high, that is because those ratings are made without a load, which can reduce current output by as much as 2/3's, which is not as big an issue with NiMH, and I will add that I have used rechargable NiMH batteries and had them perform as well as alkalines in several wireless units.