We present the results of a homogeneous X-ray analysis for 82 nearby low-ionisation, narrow emission-line regions (LINERs) selected from the catalogue of Carrillo et al. (1999, Rev. Mex. Astron. Astrofis., 35, 187). All sources have available Chandra (68 sources) and/or XMM-Newton (55 sources) observations. This is the largest sample of LINERs with X-ray spectral data (60 out of the 82 objects), and it significantly improves our previous analysis based on Chandra data for 51 LINERs (Gonzalez-Martin et al. 2006b, A&A, 460, 45). It both increases the sample size and adds XMM-Newton data. New models permit the inclusion of double absorbers in the spectral fits. Nuclear X-ray morphology is inferred from the compactness of detected nuclear sources in the hard band (4.5-8.0 keV). Sixty per cent of the sample shows a compact nuclear source and are classified as active galactic nucleus (AGN) candidates. The spectral analysis indicates that best fits involve a composite model: 1) absorbed primary continuum and 2) soft spectrum below 2 keV described by an absorbed scatterer and/or a thermal component. The resulting median spectral parameters and their standard deviations are <Γ> = 2.11 ± 0.52, < kT> = 0.54 ± 0.30 keV, < log(NH1) > } = 21.32 {± 0.71 and < log(NH2)> } = 21.93 {± 1.36. We complement our X-ray results with an analysis of HST optical images and literature data on emission lines, radio compactness, and stellar population. After adding all these multiwavelength data, we conclude that evidence supports the AGN nature of their nuclear engine for 80% of the sample (66 out of 82 objects). Tables 1 to 15, and Appendices are only available in electronic form at http://www.aanda.org