Project Server can look like the closest candidate — same family, same logic, the migration that should be the easiest one on this list.
I'd look deeper before deciding.
Move there, and you end up living and working across two Microsoft worlds — cloud and on-premises. Sometimes they're friendly to each other. Sometimes the same action that took one click in Project Online now takes ten, because the two worlds don't quite agree on how it should work.
The right target system isn't the one that feels closest — it's the one that fits your processes. Every company is different, and that's where the real decision sits.
I'm preparing a detailed comparison — pros, cons, and what actually changes in the move from Project Online to Project Server.
In the meantime: if you want to know whether Project Server is the right fit for your setup, straight from a subject matter expert — leave your contact details and I'll get back to you within 24 hours.
