Hello, thanks for a good question!
I'm definitely inspired by Temeraire series which put dragons in gears of history during Napoleonic wars. They were strategic and tactical asset, pushing war into quite different direction, with much better transport capabilities and beasts dropping on positions from air.
I'm sure that such use of dragons would drop on importance with technology development - before, you needed lucky shot with a heavy cannon to take down a beast, but with modern flak cannons, heavy machine guns and other weapons, dragons battle capabilities would be obsolete.
As creatures of intelligence average higher than humans, they'd become good officers, commandos or be used as quiet and untraceable transports, probably used by resistance movements a lot.
On the other hand, presence of dragons could slow down some developments - maybe machine flying would happen later, or with help of dragons, it would be much easier to do. Hard to say and I may try to answer it in my art!
Relationship would be mostly cooperative - I don't think it would be a perfect symbiosis, but intelligent species could get along. Even if it's quite optimistic view.