Why are the advantages to GEMMA?

And why might someone want to use it instead of other LMM implementations?

GEMMA is based on multivariate linear mixed model, which means multiple traits are simultaneously regressed on a SNP with/without covariates Thus, it can show how a SNP affects multiple traits at the same time.
Most LMMs regress one trait on a SNP with/without covariates (univariate LMM), and even if multiple traits are considered in some LMMs, they are slower than GEMMA as well as they detect less significant QTL than GEMMA does. Note that GEMMA performs only well in running 2-4 traits.