How to show a data template on a content control?

You can specify one of your templates on lower level. Something like:

<Window x:Class="WpfApplication1.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        Title="MainWindow" Height="350" Width="525">

    <Window.Resources>
        <DataTemplate DataType="{x:Type ContentControl}" x:Key="T1">
            <StackPanel>
                <TextBox Height="20" />
            </StackPanel>
        </DataTemplate>
    </Window.Resources>


    <Grid>
        <ContentControl Template="{StaticResource T1}">
            <ContentControl.Resources>
                <DataTemplate DataType="{x:Type ContentControl}" x:Key="T2">
                    <StackPanel>
                        <TextBox Height="20" />
                        <TextBox Height="20" />
                    </StackPanel>
                </DataTemplate>
            <ContentControl.Resources>
        </ContentControl>
    </Grid>
</Window>

Instead of setting the Template property, try this:

<ContentControl ContentTemplate="{StaticResource T1}" />