When should a startup react to a competitor, and when should it ignore them?

While building a competitor monitoring tool, I'm finding that collecting updates is the easy part. Deciding what matters is much harder.

If a competitor cuts its price, adds a major integration, or changes its positioning, how do you decide whether to respond? Do you have a rule for separating a real market signal from noise? Have you ever ignored a competitor move and later realized it was the right, or wrong, decision?