The official Bitwarden server: 2-4GB of RAM, mostly because of the SQL server and all of the separate containers. Probably at least two CPU cores to prevent one process from lagging everything out. 12-24GB of storage.
For Vaultwarden, the Rust reimplementation of the backend server: I don’t know, about 128MB of RAM? It’s using about 40MB of RAM on my server. It’s using about a minute of CPU time per hour for my install. Storage requirements are “the size of the docker container plus some database files”.
Both: a TLS certificate (Let’s Encrypt) and as much free space as you plan on sending through their encrypted file sharing service. Also the storage and configuration for your automated backups, of course.
Vaultwarden isn’t audited and it takes longer to get all of the features because it’s a hobby project and not an enterprise company. Bitwarden is set up to easily scale to whole company/whole enterprise usage. Vaultwarden is set up for “you and your family” scale which probably works fine for larger scales but I don’t think it’s set up for it out of the box.