  We review some counterintuitive properties of standard measures describing
quantum entanglement and violation of Bell's inequality (often referred to as
"nonlocality") in two-qubit systems. By comparing the nonlocality, negativity,
concurrence, and relative entropy of entanglement, we show: (i) ambiguity in
ordering states with the entanglement measures, (ii) ambiguity of robustness of
entanglement in lossy systems and (iii) existence of two-qubit mixed states
more entangled than pure states having the same negativity or nonlocality. To
support our conclusions, we performed a Monte Carlo simulation of $10^6$
two-qubit states and calculated all the entanglement measures for them. Our
demonstration of the relativity of entanglement measures implies also how
desirable is to properly use an operationally-defined entanglement measure
rather than to apply formally-defined standard measures. In fact, the problem
of estimating the degree of entanglement of a bipartite system cannot be
analyzed separately from the measurement process that changes the system and
from the intended application of the generated entanglement.
