How about middle ground? How about a small number in the pinned tab that counts the unread messages in your Inbox?
See the Number of New Important Messages in Your Gmail Browser Icon
To have Gmail show a count of unread messages (or unread important messages with Priority Inbox enabled) in its favicon, which appears in the browser's address or tab bar:
- Follow the Settings link in Gmail.
- Go to the Labs tab.
- Make sure Enable is selected for Unread message icon.
- To find the option fast, you can type "message icon" under Search for a lab:.
- Click Save Changes.
(Updated October 2011)