I'd say impact on the world history for Persia and Mongols was similar. Persia had longer history and bigger cultural/intellectual impact on the world, but it never dominated the world to the extent of Mongols and never had THAT succesfull military (I consider Mongols to be the best military empire in the history, regarding relative level of technology in their times, and their initial position - having no advanced tech, few numbers and nothing to begin with, their success is completely incredible).
Regarding those pop percentages, I know them and I wouldn't care about them, as I think they are unreliable estimates. With all my love for Achaemenid empire, I don't believe they had >40% of global population because for the entire human history India and China combined had around 50-60% of global population, so that would mean almost entire pop of the world was in Persian empire, Indian subcontinent and area of China. That's improbable, what about all other parts of Eurasia, Africa and Americas.
In the end it doesn't matter much because I'd put both Persia and Mongolia among top 10 most important civilisations of history, I just don't think Mongolia is much less significant. Its impact on the world was incredible, from Japan to Middle East and Central Europe, regarding military, politics, trade, knowledge etc.
I hope Mongolia and Persia will join civ6 roster very soon, they both are top priority for me.