I will say both, live chat for new customers and tickets for clients.

Live chat is always better. but most good customers understand the ticket system (usally 24 hour wait)

Clients prefer live chat but not every issue can be resolved over live chat, so it's best to offer both options

Live chat supports are really good and nice way of working which you do easily from your home.I know many people who are doing the same work.Its really nice.

I prefer a host that has both.

Live Chat is a great way if you have the staff and resources.

If you are one man show ticket system will be good for you.

I use both Live Chat and ticket system and there is nothing wierd or new in that In Live Chat customers get instant help and information exactly when time is matter. Tickets are stable and effective way to solve the biggest part of all problems but with Live Chat support is faster and better. Both are important and i think both are useful. Live Chat is not necessary but it helps with no doubt.

Livechat service will make customer trust you and focus on your website much more. Because customers think that you are available to them at any time once they need assistance in a instant.

I think definetely is good to have it, at least to resolve certain issues that perhaps can be an immediate solution. Then if it is something that takes longer time and is more complicated is good to send the ticket.

I can't think of any reason not to have both chat and ticketing system. The more avenues customers can use to contact support or sales with questions, the happier they'll be.
It's not often that you'll hear complaints from users saying there are TOO MANY support options to choose from :-)

Yes both are very important for communicating with customers!