What kind of hosting support do you like?
I don't really mind a ticket system - if it's fairly fast. Note, it can also lower the cost of the hosting. On the other hand, a live system, while convenient, is a good excuse to for a higher price - considering a person/persons have to be hired, sometimes for 24 hours a day. Anyway, on one free hosting company I saw, there was only public forum support. Well, I suppose that would work just as well - assuming the owner was quick to make replies. What drawbacks might you see in that scenario?
I like the ticket system much better. In my experience, live support tends to provide canned responses that are unhelpful. With a ticket system, it seems more likely that they will actually look at what is going on and develop an answer or legitimate response. That said, it depends on the company and how much emphasis they place of quality tech support.
My preferred support is to have live chat because it's just so much better than all other support methods. A ticket system is probably next down the list but they are only effective for some companies where the employees are actively looking at emails and responding to them extremely quickly. This is so important in a business such as hosting because your clients/customers will want quick replies to ensure their questions and issues are resolved quickly. That is why I prefer live chat, it's instant and you are much more likely to have your question answered quickly.
I find ticket support is better, because it gives the the company time to look at the issue and find out what is wrong. I have used live chat and besides the time delay when they are trying to find a solution is the fear that my internet will drop and then I lose the chat and the help.