Context. Small-scale vortices are ubiquitous structures that exist over a wide range of spatial extents in the solar atmosphere. They are considered to play an important role in the energy transport and local heating. However, numerical simulations frequently assess the effect of vortices without simultaneously considering the effects of spatial resolution and differences in magnetic configuration. Aims. We investigate the influence of different magnetic field configurations and spatial resolutions on vortex structures. We evaluate two detection methods to determine their impact on the morphology, statistical properties, and temperature profiles of vortices. Methods. We analyzed a set of six 3D realistic simulations of the solar atmosphere under three different magnetic field configurations: a small-scale dynamo and two initially vertical implanted magnetic fields of 50 G and 200 G. Three different spatial resolutions were employed: 20 × 20 × 14, 10 × 10 × 7, and 5 × 5 × 3.5 km3. We applied two vortex detection methods based on the velocity gradient tensor to all of the models: swirling strength and the SWIRL code. We performed a comparison of vortex locations obtained with the two methods, and a statistical analyses of the vortex generation mechanisms, the area covered by vortices, their number and characteristic sizes, and temperature profiles as a function of height. Results. We have confirmed that different magnetic field configurations and spatial resolutions impact the area coverage, number, and sizes of vortices. Likewise, the detection methods impact the statistics obtained. Swirling strength detects vortices with any orientation, but a height-dependent threshold is needed. SWIRL only detects vertically oriented vortices, but shows a better agreement with the rotating horizontal velocity field. Simulations with a vertical magnetic field of 50 G support the formation of chromospheric vortices without a photospheric counterpart, while most of the vortices in the 200 G model directly connect the photosphere with the chromosphere. Small-scale dynamo simulations are characterized by a large number of horizontal vortices; vertical vortices are nearly absent at chromospheric layers. The temperature profiles of the vortices confirm that they are hotter than their surroundings, regardless the simulation setup. Conclusions. Vortices are ubiquitous throughout the solar atmosphere. Their detection is affected by the methodology employed; SWIRL is a more robust method. The strength of the magnetic field and the numerical resolution considerably affect the number and size of the structures detected. Despite this, they all show temperatures higher than those of their surroundings.