One's in the past tense and one in the present, but we do use both to refer to a situation that happened in the past (the breaking of the vase!) I'm sure there's some subtle difference, but I would always use "the object is broken" if I am observing that an object is damaged, but if I am referring to the process of it breaking (having just happened) I would say "the object has broken!" I hope that makes sense and other anglos would agree...

vase is broken - разбитая ваза, и это ее состояние, которое ни на что не влияет. Это просто констатация факта. Например, в музее Вы видите разбитую вазу и говорите собеседнику, Look, the vase is broken. vase has broken - Ваза разбилась. По контексту в этом случае важно, что ваза как бы сделана разбитой. Например, вы пришли домой и увидели разбитую вазу, Вы расстроены и можете сказать Oh no, my vase has broken

Vase is broken = it means the vase is, in its current state, not in one piece. Vase has broken = it means the vase was one in one piece previously, but with the passage of time, the vase is no longer in one piece.