The truth is a little bit different. Monero is anonymous while Verge is only optionally anonymous and it is considered the privacy focused version of Dogecoin https://monero.stackexchange.com/questions/6813/what-is-the-difference-between-monero-xmr-and-verge-xvg. Also Monero can be use with TOR network even if it requires some configuration https://github.com/monero-project/monero.
The only advantage of Verge over Monero is the transaction fee of 0.1 XVG that are about 0.02 $ while for Monero about 10 $. Monero reaches 1000 tps while Verge only up to 100 tps.