Base strength of card wins.
Awarding ties based on original strength would severely weaken cards like peasants, assassin, and archer (when played as support) w/o really doing anything to solve the "you can't play a support card to gain a tie and a random draw." problem -- The player with the highest original strength -- since lowered by other support cards -- could play support cards to the point of a tie knowing that they would automatically win on that tie.
Land goes to bottom of land deck. No one wins it, it's replayed later.
That might be a viable variant in a 2 player game, but I'm not sure how well it would work in a multi-player game.
As someone who helped play test a lot of proposed tie breakers, trust me when I say the random draw always came out feeling like the best option.