The Bland-Altman limits of agreement (LOA) are widely used for assessing agreement between two measurement methods. A critical issue is to construct appropriate confidence intervals for the LOA. The exact confidence interval procedure has recently been shown to outperform two conventional equidistance-based confidence intervals for normal data. In this paper, we conduct extensive simulation studies to evaluate the performance of the exact confidence intervals and several competing approaches, including the two equidistance-based confidence intervals, bootstrap confidence intervals, and Bayesian posterior credible intervals using the Dirichlet process prior for non-normal data. We provide guidance on which confidence interval procedure to use in relation to the extent and form of departure from normality and the sample size. We illustrate the use of these procedures by applying them to a recent study conducted at MD Anderson Cancer Center of dual energy x-ray absorptiometry (DXA), as a potentially cost-effective method of measurement of visceral adiposity, as compared to the gold standard of CT scan, in gastrointestinal and pancreatic cancer patients and survivors.