Different metrics have been proposed to compare Abstract Meaning Representation (AMR) graphs. The canonical Smatch metric (Cai and Knight, 2013) aligns variables from one graph to another and compares the matching triples. The recently released SemBleu metric (Song and Gildea, 2019) is based on the machine-translation metric Bleu (Papineni et al., 2002), increasing computational efficiency by ablating a variable-alignment step and aiming at capturing more global graph properties. Our aims are threefold: i) we establish criteria that allow us to perform a principled comparison between metrics of symbolic meaning representations like AMR; ii) we undertake a thorough analysis of Smatch and SemBleu where we show that the latter exhibits some undesirable properties. E.g., it violates the identity of indiscernibles rule and introduces biases that are hard to control; iii) we propose a novel metric S2match that is more benevolent to only very slight meaning deviations and targets the fulfilment of all established criteria. We assess its suitability and show its advantages over Smatch and SemBleu.