Executive dysfunction and slowed processing speed are central cognitive impairments in cerebral small vessel disease (cSVD). It is unclear whether the subcomponents of executive functions become equally affected and whether computerized tests are more sensitive in detecting early cognitive changes over traditional tests. The associations of specific executive abilities (cognitive flexibility, inhibitory control, working memory) and processing speed with white matter hyperintensities (WMHs) and Instrumental Activities of Daily Living (IADL) were examined. In the Helsinki Small Vessel Disease Study, 152 older individuals without stroke or dementia were assessed with brain magnetic resonance imaging and comprehensive neuropsychological evaluation. WMH volumes were obtained with automated segmentation. Executive functions and processing speed measures included established paper-and-pencil tests and the computer-based Flexible Attention Test (FAT), Simon task and Sustained Attention to Response Task. White matter hyperintensity volume and IADL were associated with multiple cognitive measures across subdomains independently of demographic factors. The highest effect sizes were observed for FAT numbers and number-letter tasks (tablet modifications from the Trail Making Test), FAT visuospatial span, Simon task and semantic verbal fluency. Some of the widely used tests such as Stroop inhibition, phonemic fluency and digit span were not significantly associated with either WMHs or IADL. Processing speed and executive function subcomponents are broadly related to functional abilities and WMH severity in covert cSVD, but the strength of associations within subdomains is heavily dependent on the assessment method. Digital tests providing precise measures of reaction times and response accuracy seem to outperform many of the conventional paper-and-pencil tests.