It can extract more flavor. The most fruity and sweet brews I've ever had were good espresso shots. The same beans in a pour over are still fantastic, but it's all amplified and more pronounced when made as an espresso shot. There's also a syrupy texture that you really can't get with any other brewing method.

All that said, every day I drink pour overs and aeropress brews--I don't want to drop the $1k+ on a proper home espresso setup.