Actually wood is stronger in tensile: "tensile strength of soft- woods parallel to grain at 12% moisture content generally ranges between 70 to 140MPa. The compression strength is lower and is usually in the range 30 to 60 MPa."
Steel is similar in strength both ways, although it varies a lot depending on how it was annealed. (The harder the metal the better compression is vs tensile.)
This is true but the main concern with compression loads is buckling, which generally happens well before the material yields to normal stress. This means that compression members need to be much stiffer in bending, and so generally bulky and geometrically large, with a big moment of inertia. Whereas tension members can basically just be wire rope.
Wood can easily be built up into a much larger cross-section than steel for the same cost and less weight, so it makes sense to use it for compression loads.
Steel is similar in strength both ways, although it varies a lot depending on how it was annealed. (The harder the metal the better compression is vs tensile.)