The figure of the Earth can be modelled either by a cartesian plane, a sphere or an (oblate) ellipsoid, in decreasing order with respect to the approximation quality. Based on those models, we experimentally study the accuracy-performance trade-offs of various methods for some basic geodesic problems. For our experiments we use the open source libraries Boost Geometry and GeographicLib. Our results can be used as a reference for practitioners that want to use the most efficient method with respect to some given accuracy. Geodesic computations are building blocks for many higher level algorithms such as k-nearest neighbour problems, line interpolation, area and buffer, to name a few.