I'm a battlemaster pt pyro and my brothers a battlemaster operative and our fights go back and forth. It all really gets down to how many cds you have up vs how many cds he has, and how many both of you are willing to spend.
You may want to consider specing into 2/2 infrared sensors for stealth detection over gyroscopic alignment jets because you will have more trouble with sins and operatives regardless and with this talent you can see sins from a mile away, and operatives not smart enough to get increased stealth will be easier to pop out. If you do happen to pop the operative out of stealth you'll make work of him I'm sure.
If he's really out to get you he'll learn to pop sneak as he approaches you to ensure a opener. When he does you "don't determination out" I don't know how much I can stress that. You need to sit there and relax, and take it like a man. I know when you are getting hammered you may immediately just pop out because of the intensity involved but you can't do that. Jarring strikes - the opener, is now only 1.5 seconds long, and you don't want to waste something as valuable as determination on it.
My brother tells me it draws a smile on his face when he sees BH players trinket out of it, and also states that he worrys more when they wait to trinket out of his debilitate [a 4 second stun mirror to our electro dart].
Anyway after you take the opener you attempt to carbonize them while running away, and pop a flameburst to proc the snare. If they trinket out of the carbonize even better for you, just electro dart them right after. If they don't escape out of carbonize make sure you have enough distance, and save electro dart for a later time. Then pop whatever damage trinkets or adrenals you have to offer and begin the nukage, drop the thermal detonator to release the cd, immolation missile, and rail shot. If the operative uses his snare [sever tendon on a 12 second cd] use your energy shield to remove it so that you have full mobility, might as well pop kolto vents to regain some hp if available. Attempt at holding them at the 10metre mark so you still have access to flame burst, while keeping the operative in front of you and strafing to the side, as if you are running circles around him. So in a sense a medium range kite will do, since all the hard hitting abilities the operative has to offer are at a 4metre distance.
Do make sure however to dart in for a rocket punch whenever available, it does alot of damage and has a stronger chance of refreshing rail shot but don't stick around. At this point you flame burst spam him and rocket punch off cd, and rail shot every chance. You may get a second thermal detonator on him near the end of the fight but it may not last that long.
Now, if he uses cloaking screen [vanish] you CANNOT let him get another opener. You need to stealth scan him out, and immediately reapply flame burst. If he gets another opener it's a good chance even if you had been winning the fight, you're as good as dead.
The rest is up to the RNG Gods.