Class D amps are smaller, lighter, and run cooler than the standard class A/B amps and other designs. I'm not an EE, so it's better to do a Google search if you really want to learn the technical differences.
One thing that confuses people is the difference between the amplifier and power supply.
The very lightweight amps like the Markbass amps, Walter Woods, AI, etc. use switch mode power supplies (SMPS), which are much smaller and lighter than the big, traditional power transformers used in other designs.
However, you can have a class D amps with a large, traditional power supply (iAmp500/800 and Epi502). This results in a very cool running amp, moderate weight, and until recently, resulted in more low end ooomph than the switching power supply amps available like the Walter Woods.
On the other had, you can have a class A/B amp with a switching power supply, like the Markbass LMII and the Genz Benz Neo Pak.... small and lightweight, but some would say warmer and more natural sounding than their class D counterparts.
And of course, you can have class D and switching power supply amps, like the Markbass F1, the AI amps, the Walter Woods, the Genz 6.0/3.0 and the iAmp300... very small, very light, most don't need fans.
It's hard to attribute a tone to 'class D' amps... the F1 and Walter Woods are very quick, bright, even sounding, while the AI Focus and Clarus are warmer, darker and more organic. The Genz 6.0 has a tube in the pre, which adds another dimension.
In short, decide what weight and price you can deal with, and then use your ears. The days of class D or switching power supply amps sounding thin or harsh versus their more traditional counterparts is long gone IMO and IME


