There is growing interest in the role of structural variants (SVs) as drivers of local adaptation and speciation. From a conservation genomics perspective, the characterisation of SVs in threatened species provides an exciting opportunity to complement existing approaches that use single nucleotide polymorphisms (SNPs) to detect adaptive variation, identify conservation units, guide pairing decisions and inform conservation translocations. However, little is known about whole-genome SV frequency and size distributions, especially for small populations. To explore the impacts that SV discovery and genotyping strategies may have on characterisation of SV diversity in non-model organisms, we explore a near whole-species resequence dataset, and long-read sequence data for a subset of highly represented individuals in the critically endangered kākāpō (Strigops habroptilus). We demonstrate that even when using a highly contiguous reference genome, different discovery and genotyping strategies can significantly impact the type, size and location of SVs characterised, which indicates researchers should exercise caution when drawing conclusions at the individual-scale. Further, we find that genotyping SVs discovered with long-read data at the population-scale with short-read data remains challenging. Despite this, we found that all six strategies used to characterise SVs in kākāpō reflected similar trends at the population-scale including the identification of population structure. We are optimistic that increased accessibility to long-read sequencing and advancements in bioinformatic approaches (e.g., multi-reference approaches like genome graphs) will alleviate challenges associated with resolving SV characteristics below the species level and facilitate the characterisation of population- and individual-level SVs in threatened species around the globe.