JQL will give you always a list of issues - and only that. With SQL you can do more, aggregations, search for other things (Users, Projects, ...), etc.
See here for useful examples:https://confluence.atlassian.com/display/JIRA041/Example+SQL+queries+for+JIRA
Furthermore the differences mentioned by Udo, I would add one more:
SQL is standard while JQL is proprietary. It means that there are a lot of tools supporting SQL whereas JQL is restricted to JIRA.
Fortunately, there is an add-on (SQL for JIRA) which brings all the power of JQL to SQL. Therefore users can take all the benefits of SQL and JQL working together.
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