SomebodySubject provides somebodyIndirectObject somethingDirectObject.
SomebodySubject provides somebodyDirectObject [PrepositionPhrase with something].
The two forms are exact equivalents, they are both current and idiomatic in all registers, and there is no reason to prefer one to the other in any context.
The double forms arose because at one time provide was often used in the sense equip, taking the entity supplied as its DirectObject: one spoke of providing an army or ship, meaning to supply it with whatever it needed. In this case, PrepositionPhrase was needed to specify what “provisions” were supplied.