Both are good tools but direct feature by feature comparison is difficult. It really depends what you are trying to achieve, your budget, integration with other tools, resource to maintain it and so on.
Do you have a list of things you are looking for from a service desk tool?
Atlassian will tell you about price and speed - JSD tends to be a lot cheaper (and better integrated with development processes). My main impression is that they start at different ends - Jira Service Desk does the basics of a help desk, and then you add features you need. Service Now tries to do almost everything off the shelf, and you ignore the features you don't need.
But, I would look at the more independent stuff as well - https://www.upguard.com/articles/servicenow-vs-jira and https://www.gartner.com/reviews/market/it-service-management-tools/compare/atlassian-vs-servicenow
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