The effect of metal and support acidity on the hydroconversion of dimeric aryl ethers, used as model molecules for lignin, is still under debate, both in terms of hydrogenolysis (cleavage of the ether bond) and formation of by-products (coupling of aromatic monomers to dimers by alkylation reaction). Their role is investigated here in the conversion of three typical molecules representative of the α-O-4, β-O-4, and 4-O-5 ether linkages of lignin, respectively, benzyl phenyl ether (BPE), phenethoxybenzene (PEB), and diphenyl ether (DPE), at 503 K, under 18 bar of H2 in decalin. Ru- and Pd-based catalysts were synthesized on non-acidic SiO2 and on acidic HZSM5. Under these reaction conditions, the conversion of the ethers over the bare supports was observed in the presence of acidic sites; the effect decreased as the ether bond strength increased. The results also suggest that the product distribution is directly affected both by the support acidity and by the oxophilicity of Ru. Alkylated products from isomerization reactions, which are reported to be formed only over acidic sites, were also produced on the surface of the Ru nanoparticles.