If the common field have a finite set of values then you can create a parameter and apply that parameter to both the sheets as filter.
That way you can control both sheet with this parameter.
Only downside is that it will be a single select filter.
Hi Ben, you can use a parameter as Fulkit said, or you can actually just wait until Tableau 10 is released (which should be any day now). In Tableau 10, filters can apply across different data sources.