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At the end of Rogue One, the Rebel flagship is disabled. From an exterior shot, we can see that it is heavily damaged in several locations. Vader then decides to board the ship.
Why didn't he order his Star Destroyer (or the nearby Death Star) to blow it up? Knowing that the plans were beamed aboard the ship, wouldn't it have been more prudent to just destroy it?
According to the film's official novelisation, some murmur in the Force warned Vader not to simply order its destruction. The implication is that he unconsciously shied away from murdering his daughter.
Vader stared at the burning ship. There was death at play, suffering and fear, yes—and something entirely different. Something that repelled his withered, agonized flesh.
“Prepare a boarding party,” he said.
I would assume that from a purely logistical point of view, Vader also wanted to double-check that additional copies hadn't been made or transmitted. This is the same reason that he boards Leia's ship at the start of New Hope.
Why rely on deductions and assumptions when there's hard evidence to be gained, and an imbalance of power that minimizes risk?
Taking the ship and its occupants mostly intact preserves multiple avenues for gleaning hard evidence:
Exercising these options can more clearly establish the scope of the leak and thus narrow focus of any hardening/counterintelligence operations required to identify and secure any vulnerabilities that were exposed, as well as assess Rebel awareness and capacity to capitalize on those vulnerabilities.
There's also potential to gather additional, unrelated inteligence in the process such as: fleet movement, base locations, security codes, operational procedures, and overall enemy strength.
Short answer: Chopping up Rebels with your lightsaber is more fun than watching their ship be destroyed by turbolasers.
Long answer: Vader is consistently shown to react emotionally and place a high priority on his own agenda. He often does what he wants to do, rather than always doing what is most strategically sensible. For one thing, he's the second highest ranking person in the largest military in the galaxy and yet chooses to fly a starfighter in the Battle of Yavin. Can you imagine the Vice President of the U.S. flying a fighter plane into battle during his term in office? Perhaps he's the best pilot on the Death Star, but that implies that he pilots regularly, which isn't something you'd expect from such a high-ranking figure.
Likewise, Vader participates directly in the ground invasion of Hoth. I don't think he's on the front lines, but he is among the troopers that storm the rebel base. He also boards the Tantive IV at the beginning of ANH. He personally confronts Han and Leia at Cloud City, giving Han an opportunity to take a shot at him. Vader isn't just a commander, he's a fighter. He clearly enjoys combat and personally takes part in every operation we see under his command. He is not the type to sit back and watch the gunners cut apart the enemy ship.
You could also ask why he boards Leia's disabled ship at the beginning of A New Hope. The answer is the same.
Vader is a professional. He doesn't leave things to chance, he sees things to the end, himself. When he becomes involved, it will he his hand force-choking the information out of the captured enemies. He doesn't delegate, he doesn't trust blasters, or cannons. He's learned through experience the likelihood of a small thing escaping huge destruction.
C'mon, how many near death experiences had Anakin had as a jedi? How many exploding capital ships should have been the end of all things for him? He probably felt someone with the power of the force somewhere on board. Why else was he on his way to the Tantive IV? There wasn't even proof the plans were on there. But he felt something. And by this point, Vader trusts his feelings for these things, aged Sith he be.
