split a database web application - good idea or bad idea?
Application1 uses database1 on ServerX
Application2 uses database2 on ServerY
Both application communicates over web service API, they are apart of the same application, one application is used to manage user's profile/personal data, while the other application is used to manages user's financial data.
Or should just put them together and just use 1 database on the same server?
That's a question that nobody can answer unless we know the reason why they were split to begin with. For example, maybe the user's financial info was kept separate due to legal or contractual/standards reasons (such as PCIDSS).
Agree that it's not something we can answer. I think what one can say is that along the lines of having loosely coupled components its good that they CAN be separated, but if the situation -- costs, performance, security, etc. call for it one way or the other depends on the circumstances and judgement.