Summary: We consider certain 1/4 BPS Wilson loop operators in \(\mathrm{SU}(N)\) \( \mathcal{N}=4 \) supersymmetric Yang-Mills theory, whose expectation value can be computed exactly via supersymmetric localization. Holographically, these operators are mapped to fundamental strings in \(\mathrm{AdS}_{5}\times S^{5}\). The string on-shell action reproduces the large \(N\) and large coupling limit of the gauge theory expectation value and, according to the AdS/CFT correspondence, there should also be a precise match between subleading corrections to these limits. We perform a test of such match at next-to-leading order in string theory, by deriving the spectrum of quantum fluctuations around the classical string solution and by computing the corresponding 1-loop effective action. We discuss in detail the supermultiplet structure of the fluctuations. To remove a possible source of ambiguity in the ghost zero mode measure, we compare the 1/4 BPS configuration with the 1/2 BPS one, dual to a circular Wilson loop. We find a discrepancy between the string theory result and the gauge theory prediction, confirming a previous result in the literature. We are able to track the modes from which this discrepancy originates, as well as the modes that by themselves would give the expected result.