Live chat can be a huge asset but it can also be a huge liability. It depends how you've implemented it and the nature of your business.
If most of your support requests can be handled easily then live chat is perfect, if they require much more time I don't think you can beat tickets.
I used to host some websites with HostGator, when they removed the ability to submit a ticket forcing you to use delayed live chat I canceled my account after 7 years. In my opinion in the hosting industry support tickets can't be beaten.