Slightly off-topic here but wavelength isn't always the deciding factor in how well a laser burns or how tightly the beam can be focused. For instance, usually a CO2 laser can be focused better than a YAG (this applies more to very powerful industrial lasers) not because of wavelength (CO2 being a much longer wavelength of course) but because YAGs are usually multi-mode. It's therefore easier to focus a single-mode beam down tightly than a multi-mode one.
But of course this really doesn't apply (usually, unless you have something weird like WL's SpyderBX with it's TEM-2 modes) to visible light lasers.
There are so many variables when it comes to what (and how well) a laser will burn or cut something. For instance, my YAG makes a really explosive "pop" and flame and smoke when I hit a piece of black foam core, but if I black sharpie a piece of wood, for instance, the effect is much less, even though the black surface is actually blacker! It's a characteristic of the material.
Would make an interesting experiment if someone who had two different colored lasers outputting exactly the same mw and he/she could test the effects on various materials with a focused beam at various distances to see if the effects are the same or different. Unfortunately I don't have two lasers that output the same power (not that I know of - I've only had three of them meter-tested).