So it really depends as you might expect. But let me give you some thoughts here that might hit home for you and ultimately help you out.
The benefits of having a single board is that if the team has a relatively common goal then they can move collectively together more easily. Moreover as a scrum master or project manager in control of this board it will be much easier to work than multiple boards.
Now if the teams are very independent and will work on different schedules and they will plan their sprints individually and don't want to be bothered with the clutter of other team's backlog then multiple boards is often best. In this case you could have a scrum of scrums approach where you have a master board that gives you visibility of all the individual boards.
Personally, I tend to always start with the idea of using a single board and trying to keep it simple. I would probably start by trying to answer this one very important question - what solution will make the individual teams work is efficiently as possible? The answer to that question should drive your solution even if it means that you as a PM have a bit more overhead in your job. Your job is a PM is to insure that the project team doesn't have any avoidable barriers.
In your case maybe a single backlog will work for planning and then use either a single sprint or run parallel sprints.
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