Between 发财 and 致富, which one is more commonly used? Or is there any difference in emphasis.
致富 is a verb that's closest to "wealth creation", usually in the business or trade context. So both gambling wins and earning money from professional service (e.g. as a medical doctor) wouldn't be associated with 致富. 致富 implies wisdom, smart or cunning in money matters.
发财 is somehow receiving money or value that's slightly unexpected or associated with luck or if not luck the amount is more than usual. So picking up $10 on the street maybe "发财了" is fit. Being a medical doctor or lawyer, if described as "发财" it would imply a hint of jealousy or contempt on the part of the speaker. "发财" is morally neutral, so both a con job or receiving an inheritance can qualify. Anyway it is informal speech.
About the "Which one is more commonly used?" note that there are many other similar terms which are appropriate for different situations. 赚钱 is most common and neutral, including receiving salary for hard work or smart business.