You rightly comment that both Leopold of Belgium and Christian of Denmark remained, while Wilhelmina of the Netherlands fled, Leopold lost his throne and Christian turned his pre-war unpopularity into popularity.
Leaving aside constitutional considerations, Wilhelmina was a fiery critic of nazism in exile, but her political reform plans were decidedly undemocratic - and quickly buried. Christian resisted nazism and the deportation of jews. The story that he wore a star is apocryphal, but I have no doubt that he would have done so if the nazis would not have relented. He did restrain the resistance and showed more compassion with jews than with communists, but there was never a doubt that his sympathies were with Denmark only. Leopold, by contrast, behaved in a vacillating and pretty controversial way, leaving him open to doubt as to how far he was willing to go.