We study the prediction for the Higgs transverse momentum distribution in gluon fusion and focus on the problem of matching fixed- and all-order perturbative results. The main sources of matching ambiguities on this distribution are investigated by means of a twofold comparison. On the one hand, we present a detailed qualitative and quantitative comparison of two recently introduced algorithms for determining the matching scale [1, 2]. On the other hand, we apply the results of both methods to three widely used approaches for the resummation of logarithmically enhanced contributions at small transverse momenta: the MC@NLO and POWHEG Monte Carlo approaches, and analytic resummation. While the three sets of results are largely compatible in the low-p⊥ region, they exhibit sizable differences at large p⊥. We show that these differences can be significantly reduced by suitable modifications of formally subleading terms in the Monte Carlo implementations. We apply our study to the Standard Model Higgs boson and to the neutral Higgs bosons of the Two-Higgs-Doublet Model for representative scenarios of the parameter space, where the top- and bottom-quark diagrams enter the cross section at different strengths.