Hi,
For this, you have to write two separate actions for the menus. Right now you may have given the same action for both the menus.
Just copy the existing action of the menu and create a new action and assign it for the second menu item. In this action, you can change the default filter.
<record id="action_account_analytic_account_form" model="ir.actions.act_window">
<field name="name">Analytic Accounts</field>
<field name="type">ir.actions.act_window</field>
<field name="res_model">account.analytic.account</field>
<field name="search_view_id" ref="view_account_analytic_account_search"/>
<field name="context">{'search_default_active':1}</field>
<field name="view_type">form</field>
<field name="view_mode">tree,kanban,form</field>
</record>
Update;
As you are looking to do it from the user interface, you can follow this,
1. Duplicate the Existing Action record and assign this record as the action of the second menu.
2. Now to give new default filter for the second menu, edit the context in the action
Thanks