Some of this depends on how long it's been since your ducts were last (if ever) cleaned. Last house I had was a forced hot air house, and we had been there about 16 years before cleaning the ducts became an issue, more for dust considerations as the furnace had been replaced a couple of years prior. The contractor was able to show me some of the stuff he found in the ducts and how caked in place it was in most locations. His method of choice was similar to the brush method you describe, where a moving object was inserted into the ducts to break up the settled and caked debris so that a very large vacuum attached to the lower level of the system could suck it all out.

Not being familiar with the steam method, but quite familiar with what we saw in the ducts, I'd tend towards the moving brush. But that's just one opinion.

Thanks. I'm not sure if the ducts have EVER been cleaned, at least in the last 50 years or so. Since the former owners were smokers and had several pets, I'm leaning towards having the ductwork cleaned out before installing the new furnace and definitely before we move in. Plus...my wife has allergies.

Duct Cleaning is important, just as Carpet Cleaning and home cleaning.
http://www.canaduct.com/