While I generally agree with Wang Yang's answer, in everyday life you really cannot tell. A particular business or organization will pick the titles that they use and some use "Deputy" to actually denote a higher rank than "Vice". For example, in many banking and securities companies, there are all different levels of "vice-president" - vice president, first vice president, second vice president, senior vice president, executive vice president. In these situations, when someone has "Deputy" in front of their title, Deputy CEO, Deputy Chairman, it may actually denote a higher level position.

Vice- stresses 'next in rank or authority to' another person, it tends to be used for people with high authority. ex- vice-president, viceroy, vice admiral (these people are one step away from the top.) Deputy- stresses 'delegated or appointed to act for another person, it is used more than 'vice' in business. May be for people with lower authority. Ex- deputy manager, deputy sheriff