Currently a bitbucket user can only use already "system preset" filters or searches.
Currently they are set to be: All, Open , My Issues 'or' Watching.
These preset filters are not expandable to include users custom filters.

These filters are limiting to bitbucket users.

The bitbucket user can still accomplish a custom search from the advanced search link. However, a bitbucket user will have to "compose" a search every-time they search issues since:

• They do not have the ability to save a filter/search-query like they do in jira
• They do not have the ability to key in an issue query in the same screen: instead they have to navigate to a different screen. (you have still do it from the url query string...)

it would be nice for atlassian to add this feature. it will make the issue tracker more usable and they wouldn't feel that they have to use jira for every repo.