I would say that normal peasants would would be terrified of the dragons of a nearby kingdom. The Sovereign dragons would scare them enough, they can take what they want and the peasants can do nothing about it. However, the neighboring kingdom has dragons in it's army. Soldiers are scary enough, but you can recognize them and know that if your army is around they can protect you from them. But a huge flying beast could rampage through a small company of men with little trouble (whether or not they have ever done so or even if they would is irrelevant). They are huge carnivores that could be sent against them.
Because of this I think most surrounding kingdoms would be very wary about them and might be plotting to bring them down. This could include the Sovereign's because it could be an unnatural situation and the partnership could make both groups (tame dragons and humans) to be much, much stronger with the ability to dominate the others. So either they will try and be close ally's or plot destruction (and maybe try to coerce some dragons to their kingdoms).