Is there a way to do a comparison on object type for a trigger?
If you are in a position to modify the (base) type assigned to 'SelectedItem' by adding the property:
public Type Type => this.GetType();
Then you could use the DataTrigger in xaml like this:
Advantage compared to AndyG's good answer is, that you do not have a magic string of your type in XAML, but have everything compile safe. Disadvantage: You need to modify your model - which might not always be possible.