  In statistical estimation theory, it has been shown previously that the
Wigner-Yanase skew information is bounded by the quantum Fisher information
associated with the phase parameter. Besides, the quantum Cram\'er-Rao
inequality is expressed in terms of skew information. Since these two
fundamental quantities are based on the concept of quantum uncertainty, we
derive here their analytical formulas for arbitrary two qubit $X$-states using
the same analytical procedures. A comparison of these two informational
quantifiers for two quasi-Werner states composed of two bipartite superposed
coherent states is examined. Moreover, we investigated the decoherence effects
on such quantities generated by the phase damping, depolarization and amplitude
damping channels. We showed that decoherence strongly influences the quantum
criteria during the evolution and these quantities exhibit similar dynamic
behaviors. This current work is characterized by the fact that these two
concepts play the same role and capture similar properties in quantum
estimation protocols.
