To fold on biologically relevant time scales, proteins have evolved funnelled energy landscapes with minimal energetic trapping. However, the polymeric nature of proteins and the spatial arrangement of secondary structural elements can create topological traps and slow folding. It is challenging to identify, visualize, and quantify such topological trapping. Designed proteins have not had the benefit of evolution, and it has been hypothesized that de novo designed protein topologies may therefore feature more topological trapping. Structure-based models (SBMs) are inherently funnelled, removing most energetic trapping, and can thus be used to isolate the effect of protein topology on the landscape. Here, we compare Top7, a designed protein with a topology unknown in nature, to S6, a naturally occurring ribosomal protein of similar size and topology. Possible kinetic traps and the energetic barriers separating them from the native state are elucidated. We find that, even with an SBM, the potential energy landscape (PEL) of the designed protein is more frustrated than that of the natural protein. We then quantify the effect of adding non-native hydrophobic interactions and coarse-grained side-chains through a frustration density parameter. A clear increase in frustration is observed including side-chains, whereas adding hydrophobic interactions leads to a narrowing of the funnel and a decrease in complexity. The most likely (un)folding routes for all models are derived through the construction of probability contact maps. The ability to quantitatively understand and optimize the organization of the PEL for designed proteins may enable us to design structure-seeking landscapes, mimicking the effect of evolution.