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Abstract We revisit the problem of matching the strong coupling expansion of the 1 2 $$ \frac{1}{2} $$ BPS circular Wilson loops in N $$ \mathcal{N} $$ = 4 SYM and ABJM gauge theories with their string theory duals in AdS5 × S 5 and AdS4 × CP 3, at the first subleading (one-loop) order of the expansion around the minimal surface. We observe that, including the overall factor 1/g s of the inverse string coupling constant, as appropriate for the open string partition function with disk topology, and a universal prefactor proportional to the square root of the string tension T, both the SYM and ABJM results precisely match the string theory prediction. We provide an explanation of the origin of the T $$ \sqrt{T} $$ prefactor based on special features of the combination of one-loop determinants appearing in the string partition function. The latter also implies a natural generalization Z χ ∼ ( T / g s $$ \sqrt{T}/{g}_{\mathrm{s}} $$ ) χ to higher genus contributions with the Euler number χ, which is consistent with the structure of the 1/N corrections found on the gauge theory side.