There is a dataset that contains body mass ($x$) and metabolic rate ($y$) from many different organisms. It is common to fit the data to the model of the form $y=ax^b$ and estimate the parameters $a$ and $b$. In doing so, it is also common to log transform $y$ and $x$ and create the linear relationship log($y$)=log($a$)+$b$log($x$) and perform linear regression analysis based on the log transformed data. Is this approach better than directly estimating $a$ and $b$ based on nonlinear regression for $y=ax^b$ (because results are different)?

There is a dataset that contains body mass ($x$) and metabolic rate ($y$) from many different organisms. It is common to fit the data to the model of the form $y=ax^b$ and estimate the parameters $a$ and $b$ (see Kleiber's law and The Metabolic theory of ecology). In doing so, it is also common to log transform $y$ and $x$ and create the linear relationship log($y$)=log($a$)+$b$log($x$) and perform linear regression analysis based on the log transformed data. Is this approach better than directly estimating $a$ and $b$ based on nonlinear regression for $y=ax^b$ (because results are different)?