As a UI view / control, the Callout is platform-specific. On Xamarin platforms we provide the CalloutStyle class to control the look of a callout on the GeoView. In WPF and UWP we use the standard XAML based mechanisms for updating control styles which is a richer and more natural way to style the UI.
To change the style of a callout, add a new style to your XAML page that declares the MapView - something like this:
<Style TargetType="{x:Type esri:Callout}">
<Setter Property="Padding" Value="24" />
<Setter Property="Background" Value="LightBlue" />
<Setter Property="BorderBrush" Value="DarkBlue" />
<Setter Property="BorderThickness" Value="4" />
</Style>
You can also override the Callout's ControlTemplate:
<Style TargetType="{x:Type esri:Callout}">
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="esri:Callout">
<Border Background="LightGreen" BorderBrush="Green" BorderThickness="4"
CornerRadius="30" Padding="20">
<ContentPresenter />
</Border>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
I hope this helps. Also note that we'll be working on filling out our Callout samples in the coming weeks so you'll have a clearer picture of how they're best used.