I’m currently running a remotely deployed OH at my dad’s house to keep an eye on him and have experience with both approaches.
You do not provide enough information about how you want to use this remote version. Is it completely stand alone or does the apartment need to work with the other OH instance? If it’s stand alone I’d go for a separate instance at both locations.
If want to either federate your OH instances (see MQTT 2.5 Event Bus and I’m currently working on a reusable library implementation) it’s not hard to set up but it does add a bit of complexity in overall design and mental load required to think about your system. For example, all the Items you want to share between the two instances need to be defined in both OH instances and kept up with each other.
And even if your devices are all network based, keep in mind that usually a VPN tunnel ends up on a different subnet which will prevent some automatic discovery features of some bindings from working if you use one central OH instance for both locations.