No, brittle materials like concrete are famously weak in tension and strong in compression. Ductile materials are generally equally strong in both. I can't think of any material offhand that's stronger in tension and weaker in compression.
Buckling is not a material failure, it's a structural failure. In pure buckling [0], the strength of the material is not actually a factor in whether something buckles or not. In most cases, material failure does occur as a side effect of the buckling, but not always. (The material's stiffness does matter, though. All else equal, something that's more flexible will buckle sooner than something stiff.)
