As far as I know, there is no performance lost as far as overhead and whatnot. It mostly depends on what you have installed. You can turn desktop Ubuntu into server Ubuntu by installing the same security/monitoring/visualization programs. The server edition just comes with a better set of pre-installed packages suited to a secure, easily maintained server.
Either way, I would recommend NOT installing X server and a desktop environment (GNOME, KDE, etc). This reduces boot time and memory/CPU usage.
Ensuring system still works... [ OK ]
Making up fake text... [ OK ]
Deploying Ubuntu Server payload to OP...
> 48:65:6c:6c:6f:20:77:6f:72:6c:64:2c:20:68:6f:77:20
> 61:72:65:20:79:6f:75:20:74:6f:64:61:79:3f:20:41:72
> 65:20:79:6f:75:20:65:6e:6a:6f:79:69:6e:67:20:74:68
> 65:20:76:69:65:77:3f:00:00:00:00:00:00:00:00:00:00 [ OK ]
Compressing the analog RSS application... [ OK ]
Synthesizing the unicode MAC protocol... [ OK ]
Sending the fiber optic alarm into the feed... [ OK ]
Rebooting the redundant CD-ROM program... [ OK ]
Connecting the RX circuit to compress neural array... [ OK ]
Writing VB script to track killer's IP address... [ OK ]
Writing answer... [ OK ]
Congratulations! By simply reading this post, you now have Ubuntu Server!
No, really, I'm serious here. The only major difference between Ubuntu Server and the regular version of desktop Ubuntu is the fact that Ubuntu Server does not come with a graphical interface or any sort of graphical "quality-of-life" improvements. As you can see on the list of things installed by default, there really isn't anything there except for the standard loadout. From the official documentation:
There are a few differences between the Ubuntu Server Edition and the Ubuntu Desktop Edition. It should be noted that both editions use the same apt repositories, making it just as easy to install a server application on the Desktop Edition as it is on the Server Edition.
The differences between the two editions are the lack of an X window environment in the Server Edition and the installation process.
Meaning, you can just install any server-related packages and everything will work for the most part. For example, if you want to install NGINX, any guide (like this one from DigitalOcean) will work perfectly fine. In the unlikely case that you don't have something you need installed, it will be when it needs to be. You can trust apt's dependency resolution system to resolve any (unlikely) problems that come up from you not having some server-standard package installed.
The only catch is that you may need to reconfigure the occasional config file to prevent a conflict (NetworkManager is infamous for this), which is not really that involved of a process at most times. You might also need to punch the occasional hole in your firewall or set up some port-forwarding, but that's pretty easy and you (probably) would have had to do that on your server install already.
So, in short, just use apt like normal and install whatever packages you want.
Best Answer
It's possible to do it the other way around, but I've never seen anyone who was able to do this simply by installing a metapackage or something.
Your best bet is either: