AJAX TabContainer has quite a few problems. This article gives a good idea of how to work around some of these problems. The most annoying problem is not able to set the styling of the TabContainer tabs. Here is a good link to overcome the problem by tinkering with the source code. The link examines the CSS emitted by the TabContainer and modifies the styles in the target page.

Another annoying feature of the TabContainer is the ActiveTabChanged event. If the TabIndex is changed by clicking on the tab, there is no AJAX styled postback. This prevents refreshing GridViews if grids are embedded within the TabContainer. Here is a good post of how to ensure that the server side ActiveTabChanged event is raised.