One of the "Cons" from live-viewing off such large sensors, is the fact that when one is feeding LV through the main sensor, the sensor is heating up, resulting in digital noise that will make its way into the image, that would not be present during a normal non-LV exposure. I am assuming the newer implementations have got highly efficient Noise Reduction routines on the sensor, to take care of this.
Essentially, unlike a split-second exposure, now you are clocking the data off the sensor, dozens of times every second and feeding it to the LV screen, consuming a considerable amount of power, while also generating digital noise.
A CCD would consume a lot more power than a CMOS and thus a CMOS is a better fit when it comes to LV, especially with a large sensor like those used in a dSLR. The other advantage with a CMOS sensor is the ability to accomodate Noise-Reduction circuitry on the sensor, unlike a CCD that is incapable of accomodating such circuitry on the sensor. This on-sensor NR circuitry will enable the reduction of the inevitable digital noise being generated via Live-view.
Think of LV as an extremely long exposure, prior to the actual click. The more you delay prior to the click, by fiddling around with the settings, the more you are heating up the sensor.
Having said this, having LV as a tool is definitely a plus over not having this as an option at all - just don't assume that there are no ill effects from clocking data off such large sensors, hundreds of times, in a short period of time. Like any other tool, use it wisely.