It depends on the seriousness of the issue. When I had an issue deliveing tickets, I called and explained the situation to them. I just wanted to get my story documented clearly. The lady was very nice.
When I have to talk to them about a sale or a quick note to add to the record, I use the chat. it's a good tool if you want to get something documented in writng.
Sometimes, if you call them, the might put you on hold and try to reach out to the buyer.
This is a great question and like other have mentioned, it depends on the issue. It's also sometimes similar to calling Verizon--you get different answer depending on who you speak to. Last week I needed a UPS delivery switched to PDF, I mean, I could have mailed the PDF but there are less issues with just uploaded the PDF's. The Chat rep told me that he had to email the buyer and they could cancel... I called in later and asked--switched it with no issue or questions.
I guess if you dont get the answer you want, try to call if you were chatting previously... Calling seems to be easiest if there is a short wait time on hold.
However, if I have needed an event added or needed something done and know it will get done, using the message board has reaped the best results for me. I called in for months trying to get an event added and I finally found this message board and it was added within a week... Now things get added within a day or two--usually.