A flat sheet and a trifold board cost roughly the same and behave completely differently. The choice is decided by whether the board has to stand on its own.
When a flat board is enough
Flat poster board is the right answer whenever something else is holding it up — a wall, an easel, a pin board. It gives you an uninterrupted surface, which matters if a single large diagram or photograph has to run across the whole thing without a fold cutting through it.
When you need the fold
A trifold stands unaided on a table, which is why science fairs, school projects and small trade tables use them. The two wings also give the display rigidity, so it survives being knocked. The cost is layout: you now have three panels and two creases, and anything that straddles a crease will look broken. Plan the content panel by panel rather than treating it as one wide canvas.
Practical points
Measure the table before you buy. A full-size trifold needs more depth than a narrow school desk offers once it is opened out. If the board will be carried between home and venue, a fold is also what makes it portable — a flat board of the same area has to travel as an awkward flat sheet that creases if it flexes.