According to Gordon Smyth group publication from 2016 "the glmQLFit and glmQLFTest functions, which are alternatives to glmFit and glmLRT. They replace the chisquare approximation to the likelihood ratio statistic with a quasi-likelihood F-test, resulting in more conservative and rigorous type I error rate control." You can find this reference at the end of the edgeR user's guide. In short: glmQL version is the latest best option according to the authors. Is it really much different from the others I cannot say, it depends on the data
What is the key difference between glmfit and glmqlfit and how do you decide which one to do? Is it related to your design?
According to Gordon Smyth group publication from 2016 "the glmQLFit and glmQLFTest functions, which are alternatives to glmFit and glmLRT. They replace the chisquare approximation to the likelihood ratio statistic with a quasi-likelihood F-test, resulting in more conservative and rigorous type I error rate control." You can find this reference at the end of the edgeR user's guide. In short: glmQL version is the latest best option according to the authors. Is it really much different from the others I cannot say, it depends on the data