Secure boot (With TPM) will save you from attacks like evil maid, Modifying bootloader, Key leaking etc.
FDE on the other hand will provide you protection from data leakage in better way comparatively from Partition based encryption. For e.g. in partition based encryption some file can end up in temporary storage and can be recovered if HD is stolen.
Now the second question where you mention that what if you encrypt the partition and someone has access to running server? In this case, if the partition is already decrypted, anyone with sufficient privileges can access all the content of the partition.
If you put a password based protection on partition, it will protect data until you do not decrypt the partition with password. So, this can provide you some protection. You just have to make sure to use partition on need basis and as soon as your work is complete unmount the drive.
However, even in this case if someone access running server then they can install the keylogger and get the password.
With FDE and secure boot, once the system is up, the logged-in user will have access to the data (depending on the privileges) since the whole drive is decrypted . So, if you want some level of restriction there as well, you can configure FDE+Secure Boot + encrypted folder. Wherein for accessing the folder after secure boot requires password. This use case is useful if you share a machine with multiple user.