Preferential flow has been hypothesized as an important factor for chemical leaching from tile-drained agricultural fields with structured soils originating from glacial till sediments. Previous studies showed that one-dimensional single-porosity models (1D-SPM) failed and that one-dimensional dual-permeability models (1D-DPERM) were limited in explaining both Br leaching and residual Br distribution, although tile water outflow peaks could somehow be reproduced. The objective of this paper was to analyze the tile outflow and leaching patterns using a two-dimensional (2D)-DPERM and a standard 2D-SPM for comparison. Flow and transport were simulated in a 2D vertical cross-section of 5.9 m length and 2 m depth using previously tested parameters. Simulated drainage rates and Br-effluent concentrations were made comparable with collector data from a field experiment by weighing results for irrigated and nonirrigated plots according to their area fractions. The 2D-DPERM simulations for surface application of Br in dissolved form in both domains overestimated the observed initial outflow concentration peaks, in contrast to closer approximation of observations assuming Br application in the soil matrix domain only. The simulated 2D mass transfer rate distribution showed most intensive exchange between domains near the water table and in the topsoil. Results from the 2D-DPERM analyses suggest that conditions at the soil surface, near the water table, and of the field-scale mixing are significantly affecting leaching patterns, in addition to local nonequilibrium effects. Here, the description of preferential flow toward tile drain could be strongly improved with the 2D-DPERM compared with the 2D-SPM. Further improvements remain challenging with respect to DPERM numerical modeling and field experimentation, with special attention toward soil structure and soil surface conditions.