A full reading for Tiger × Leo meeting Rat × Capricorn is on the way. In the meantime, the score above is computed from the canonical element matrix and sign-cycle distance, and the profiles below cover each side individually.
The very fact that the Tiger/Leo would vote itself Monarch of the World in a second is indicative of the problems in your life, the primary problem of which is that you're just too damn wonderful for your own good. This has a tendency to leave you miserable in your royal Leo's isolation, as others often feel they aren't good enough to share the same air you breathe.
Power for its own sake, and the cold brutal solitary serenity that accompanies such an exalted position, are precisely what the Rat/Capricorn lives for. If they think they've seen goals-oriented people in action before, they haven't seen anything until they've seen the Rat in you breeze past them on your way to the top, in such a way as to make Genghis Khan seem mild-mannered, of whatever hierarchy to which you see fit to belong.