JIRA Client is not a full substitute for JIRA's web interface. It addresses most of use cases and we're working on supporting every feature that you request. Yet the current version has limited functionality.
Currently, JIRA Client can download and handle effectively up to 40,000 issues.
If you have more issues in JIRA, that's ok unless you work with each and every issue. Use queries to download issues only for your project, or only open issues, or use whatever filter that defines which issues you are working with.
If you need to work with more issues anyway, give it a try. JIRA Client won't stop on issue number 40,001, though it may seem slower and require more memory.
Following is the list of standard JIRA features that are not supported by JIRA Client (as of version 3.5):
When you find out that you can't do something with JIRA Client, you can always press F9 and JIRA Client will take you to the issue's web page in JIRA. You have to be online, of course.
You are also welcome to request a feature that you need.