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Approaches based on linear mixed models (LMMs) have recently gained popularity for modelling population substructure and relatedness in genome-wide association studies. In the last few years, a bewildering variety of different LMM methods/software packages have been developed, but it is not always clear how (or indeed whether) any newly-proposed method differs from previously-proposed implementations. Here we compare the performance of several LMM approaches (and software implementations, including EMMAX, GenABEL, FaST-LMM, Mendel, GEMMA and MMM) via their application to a genome-wide association study of visceral leishmaniasis in 348 Brazilian families comprising 3626 individuals (1972 genotyped). The implementations differ in precise details of methodology implemented and through various user-chosen options such as the method and number of SNPs used to estimate the kinship (relatedness) matrix. We investigate sensitivity to these choices and the success (or otherwise) of the approaches in controlling the overall genome-wide error-rate for both real and simulated phenotypes. We compare the LMM results to those obtained using traditional family-based association tests (based on transmission of alleles within pedigrees) and to alternative approaches implemented in the software packages MQLS, ROADTRIPS and MASTOR. We find strong concordance between the results from different LMM approaches, and all are successful in controlling the genome-wide error rate (except for some approaches when applied naively to longitudinal data with many repeated measures). We also find high correlation between LMMs and alternative approaches (apart from transmission-based approaches when applied to SNPs with small or non-existent effects). We conclude that LMM approaches perform well in comparison to competing approaches. Given their strong concordance, in most applications, the choice of precise LMM implementation cannot be based on power/type I error considerations but must instead be based on considerations such as speed and ease-of-use.