Which is better for clearing blockages? Plumber's snake (aka toilet jack/electric eel) or high pressure hose?

The high pressure water jet does a great job at clearing clogs caused by water soluble objects (paper, fecal matter, soap residue, etc). Further it does a good job of clearing away residue from the sides of the drain lines. However, your friend is correct. It will not cut through large roots that may have grown through the main line. The plumbers snake does have a "saw" attachment that can cut through roots. But if your problem is a root through the drain line you have bigger problems than a clog. Consider getting a visual inspection. Some plumbers carry a fiber optic camera system they can snake through the drain and look at what the problem is. If you have done this and KNOW that roots are the problem, the ultimate solution is to have the section of drain replaced.