The Oracle database is a beast, both in terms of performance, performance tuning and features.
It probably out performs MySQL and Postgres in most areas - and if you don't do horizontal scaling, then Oracle is probably your best bet if you want to get the most out of a server.
I don't think there are any advantages of going to vertical scaling over horizontal scaling these days.
Relational databases don't scale horizontally all that far because of the challenges in replicating writes. Either you do delayed replication and have inconsistent slaves, or you do sharding and have a complicated app layer.
The trick to scaling a sql db is to either shard it and treat it like nosql with worse tooling, or go vertical as far as you can before you go horizontal. Luckily, there aren't many workloads that require horizontal scaling. Stackoverflow can run on a single beefy db server.
It probably out performs MySQL and Postgres in most areas - and if you don't do horizontal scaling, then Oracle is probably your best bet if you want to get the most out of a server.
I don't think there are any advantages of going to vertical scaling over horizontal scaling these days.