> What is the relationship between Merkuro, KOrganizer and KMail?
Both projects (Merkuro and Kontact) are what are called groupware suites of apps produced by KDE. Both projects share developers, frameworks and many breakthroughs in one translate to the other.
> Why should I choose one over the other?
A question of preference. Kontact favours implementing everything and the kitchen sink at the cost of complexity. Merkuro aims for ease of use and style.
Hope that helps.