For a Uniform $\displaystyle U(0, \theta)$

The Maximum Likelyhodd Estimator of $\displaystyle \theta$ = $\displaystyle X_(n) $

Also, the sufficient statistic for $\displaystyle \theta$ is $\displaystyle X_(n) $

and E[X] = $\displaystyle \frac{\theta}{2}$

Then the estimators of $\displaystyle \theta$ are found out as

$\displaystyle \hat \theta$ = $\displaystyle 2 \bar X$

and

$\displaystyle \hat \theta = \frac{n}{n+1} \theta$

Which one is the better estimator? What is the process to find it?

I am wondering if the answer involves calcuating the variance.