In this paper we explore multi-dimensional preference estimation from imprecise (interval) data. Focusing on different multi-criteria decision models, such as PROMETHEE, ELECTRE, TOPSIS or VIKOR, and their extensions dealing with imprecise data, preference modeling is examined with respect to a suggested set of axioms. Their performance is evaluated and some specific problems are identified, regarding the satisfaction of the proposed axioms as well as some difficulty on how to properly understand the uncertainty of the interval-valued outcome and its respective preference situation. In consequence, the Weighted Overlap Dominance (WOD) method is examined, which has been explicitly designed for interval data, thus satisfying the proposed axioms, and clearly identifying the preference relational situation for all pairs of alternatives.