If yes, I want to make sure consistency is maintained in both the applications. Also, let me know if I can use labels or components. I also have a team which create web services for these projects which are common for both.
Both may be viable options. My rule of thumb is that each deliverable product should be its own project in Jira, which enables more effective use of the built-in functionality around components, releases, and versioning.
If you are building the applications independently, using native programming languages, then two projects is definitely the way to go. If you've got two separate code bases that leverage native technologies, you may end up able to support different functionality in each application. You may also have more freedom to follow device-specific user interface guidelines, which would require different UI mockups to be attached to guide developers. And since you have separate code bases, you may have bugs in one product or another, and these bugs may drive patch releases (new versions) of the app for one device, but not the other.
If you are using a framework that enables you to target multiple platforms with one codebase, then perhaps it's OK to consider one project. If you decide, in the future, to spin off and go native, then you can follow the suggestions above and have one Jira project for each deliverable entity. You may continue to maintain your existing framework-based app for a while, while managing two additional native projects, until their hit a state where they can take over.
In both cases, I would use a separate project for your web services. If you have a requirement or bug that depends on changes to the web service, Jira allows you to link the issues and identify that one issue depends on another. Various plugins can also add functionality to these links, to let teams know when a dependency has been resolved, for example.
If you are looking for a consistent feature set across both, it feels like you would get more value out of treating them as the same backlog. I would consider actually going a set further and making " works on Android and iOS" part of the definition of done so that a story like As a user, I would like to see a record of past actions" would only be done when it worked on both.