Bioresources are used in different production systems as materials as well as energy carriers. The same is true for fossil fuel resources. This study explored whether preferential resource usages exist, using a building insulation system as an example, with regard to the following sustainability criteria: climate impact, land, and fossil fuel demand. We considered the complete life cycle in a life cycle assessment-based approach. The criteria were compared for two strategies: one used natural fibers as material and generated production energies from fossil fuels; the other generated production energies from bioenergy carriers and transformed fossil resources into the insulation material. Both strategies finally yielded the same insulation effect. Hence, the energy demand for heating the building was ignored. None of the strategies operated best in all three criteria: While cropland demand was lower in the bioenergy than in the biomaterial system, its fossil fuel demand was higher. Net contribution to climate change was in the same range for both strategies if we considered no indirect changes in land use. Provided that effective recycling concepts for fossil-derived insulations are in place, using bioresources for energy generation was identified as a promising way to mitigate climate change along with efficient resource use.