Following steps explains how you can change the tabs order on the Search Center in SharePoint 2010.

Here is how my Search Center displays. It has All Sites and Directory.

 

 

 

 

 

Click on Site Actions-> View All Site Content

 

 

 

 

 

Click on Tabs in Search Pages

The Tabs in Search Pages list displays as follows

 

 

 

 

 

Click on List Ribbon

 

 

 

 

 

Click on List Settings

 

 

 

 

 

Click the url at the top and change listedit.aspx to reorder.aspx

 

 

 

 

 

I moved directory to order 1.

 

 

 

 

 

Click Ok.

The list will show it based on the position you set. But on the Search Center it will not show the right order. It will still display as –

 

 

 

 

 

Go back to the Tabs in Search Pages by Click Site Actions->View All Site Content and click on Tabs in Search Pages. Edit the Directory Item and just click on Save. Your screen should display as –

 

 

 

 

 

If you are interested in the Search Center displaying the Directory Search by default, you can change the welcome page as follows –
Click on Site Actions -> Site Settings

 

 

 

 

 

Click on Welcome Page

 

 

 

 

 

Click on Browse button

 

 

 

 

 

 

 

 

Click on People page and click ok.
Click Ok on the Welcome Page.
Now the Search Center will display the Directory Tab by default.