For a proportion, is $\displaystyle \hat{p} \pm z_{\alpha/2} \sqrt{\hat{p} \hat{q}/n} $ better than

$\displaystyle \frac{\hat{p} + \frac{z_{\alpha/2}^{2}}{2n} \pm z_{\alpha/2} \sqrt{\frac{\hat{p} \hat{q}}{n} + \frac{z_{\alpha/2}^{2}}{4n^2}}}{1 + (z_{\alpha/2}^{2})/n} $ in terms of precision and reliability?

Wasn't the first used a lot in the past?