Live chat is best for quick answers
Pre-sale questions, checkout problems and simple how-to questions are usually solved in a few messages. Live chat keeps those conversations short.
Ticketing is best for long problems
Refunds, technical bugs and anything that needs several people are easier to track in a ticket with a clear history.
Using both
Many teams start with live chat on the website and send long cases to a ticket. Make sure the chat history can be searched, so nothing gets lost when a case moves.