I would argue that the modern day military would have to monumentally screw up in order to not wipe the floor with the 1600s era military. 

Chances are they would not even have to meet the enemy in the field. All it would take is a show of force with a flight of aircraft bombing their capital- that should be more than sufficient to make it clear to the leaders of the continent that it's in their best interest to not resist. While they may not care about the lives of their citizens, the fact that you can put a 1,000lb bomb on a warlord / king's heads anywhere in the continent would make them bend their knee quick enough.

The enemy military would likely be armed with smooth bore muskets, with a range of maybe 100 yards at a pinch, and a rate of fire of maybe a couple of rounds per minute. Couple that with cavalry and cannons, they would have pretty much no hope against a modern military.

I think you may be underestimating how deadly modern military equipment is. Consider how deadly crossing no-mans land in WW1 was.

Now imagine that one side has modern weaponry, and the other side has muskets. All it would take is a couple of incredibly bloody battles for the peasants to learn that trying to fight is a death sentence, and the 1600s era nation now longer can field an army.