Power meters give more instant feedback about what you are doing – with heart rate you can ease off for a bit before it reacts, or it takes a while to catch up when you increase your effort. Generally I find training with power (on a turbo) more intense, as if I’m easing off I know within a second or so.
General concept of training with power is similar though, although there are some books that use different ways of working out training plans based on expended power in a session.
So to answer your question – yes, more accurate and detailed, but not cheap – depends how serious you are. I know a few people who use powertaps now.