uniqueness of Hodge decomposition

Question

Is it true that there is some kind of uniqueness associated with a Hodge decomposition.

E.G. if X and X' have isomorphic Hodge decomposition:($H^i(X,\mathbb{C})= \oplus_{p+q=i}H^{pq}(X)$) $\cong$ ($H^i(X',\mathbb{C})= \oplus_{p+q=i}H^{pq}(X'))$, then $H^{pq}(X)\cong H^{pq}(X')$?