Different filter settings in report tabs of Google Analytics Custom Reporting?

You cannot have different filter settings in different report tabs of a custom report in Google Analytics.

You can, however, create a Dashboard in the new Google Analytics interface that has a different filter applied to each widget.

I have created an example dashboard here. Browse to the GA profile you would like to add it to, then paste this link:

https://www.google.com/analytics/web/permalink?type=dashboard&uid=6p26M4W7SCWy0W1bFKvNSQ

It should create two widgets, one named 'Visits to home page' and the other named 'Visits to /[Pp]age/.*'. It's giving nice results for me - let me know if it works for you.