Why do people always assume gun-powder = guns? You won't see guns first. You'll see rockets. Any retard can make one, they can be mass-produced and used enmasse as either a siege tactic or simply against a mass of infantry in a field. Would it be very effective? Well, in a siege situation, yes. Big explosive thing that's on fire against...mostly flammable structures. Know what else you get? Much easier mining. Easier mining means you can field larger, better-equipped armies. More armies equals more power-projection. And while I doubt we'll be seeing a space program in 1300, we will see a far more advanced..and dare I say it, steam-punkish(or 'gunpowder punk') civilization.
On the downside, alot more people are going to die. And if the Romans do develop it first as rockets, they might very well be seen as gods or, atleast, extremely powerful magicians by the less advanced nations/tribes of the world.