I have not had a lot of support experiences with Atlassian, but of the few I have, I wasn't very satisfied with the results. I found that multiple people would respond to the issue at various stages, requiring re-communication (even though the support system stores everything and shows it to both them and you). Often responses came at odd hours, resulting in 24+ hour turnaround on basic responses, even if you respond right away. Support often asks you to do things which require downtime, and don't seem sympathetic if your organization requires that downtime to be done off-hours. This makes it difficult to resolve issues in a timely manner, if at all.
I must note that I have not opened a support incident with them in close to 2 years, and it's my understanding from colleagues that there has been much improvement. My comments and ratings reflect my older experiences.