When Vader first attempts to board the Rebel Blockade Runner at the end of Rogue One, we see Vader board first. After he slaughters several Rebel soldiers, we see that his Stormtroopers have come behind him. Now this is the exact opposite of what happens at the beginning of A New Hope; the Stormtroopers go ahead of Vader and several of them get killed.
Darth Vader is not afraid of a couple of Rebels... and he doesn't board Tantive IV until Tatooine.
The MC75 cruiser Profundity, owned by Admiral Raddus, was the ship that received the "stolen data tapes." It's disabled by the Star Destroyer Devastator, at which point Vader and stormtroopers board to locate the data.
At this time, the Empire is not aware of the blockade runner located in the docking bay of Profundity.
Once Darth Vader becomes aware of Tantive IV, he figures out where the tapes are going, and makes a mad dash to catch them; he's in front of his stormtroopers because he doesn't have time to wait. He's got the skills and speed to mow through a handful of retreating troops scrambling to evacuate... but even with his head start, he comes up short at the airlock as Tantive IV escapes.
The situation is way different when they've caught up with the blockade runner and board her. For one, he's not chasing after a few scrambling rag-tag rebels throwing wild shots behind them. Darth Vader is boarding an enemy ship, from a known entry point, through unknown defenses, with defenders who are expecting him, and who have entrenched defenses, and unlike before, he doesn't know where exactly the tapes are.
Sure, Vader is such a bad-ass he could probably have pulled a Kool-Aid man and charged through the door, but it's way more prudent to let a Forlorn Hope squad through at first, to breach the doorway and set up a beachhead. He'll need a lot of troops to search the ship, anyway.
We're most likely never going to see that missing 10mins between Rogue One and New Hope, but I thought this was strange at 1st too (Mostly because of my lust to see Vader slaughtering people). Then it hit me though, Vader boards with a party of a couple small ships. The Tantive IV jumps to into hyperspace with Vadar watching still on the rebel ship that the Tantive IV detached from right? In New Hope the Tantive IV is pulled in by a tractor beam of a Star Destroyer. So connecting the dots, the Tantive IV makes the jump, the Star Destroyer immediately follows, Vader has to return back to his ship, make the jump himself and because he's a few mins behind, shows up a little late to the party. Which explains why the stormtroopers have complete control of the ship before Vader gets there.
One thing to keep in mind is also the personality of Vader. He is still like Anakin. Thus he does not lead from the safe back but instead from the front. And his fall to the dark side also brought out more brutal tendencies than anything else...thus he is even more prone to lead from the front.
In rogue one the ship is boarded after getting disabled. Vader naturally was among his men there and boaded the ship. Rushing towards the data as fast as possible when he found out where it was. Then it escaped.
As he had to reach the rebel flagship with his troops it can be assumed that they used shuttles to do so. Thus he had enough time to land/board at the same time as his troops.
The next time the Tantive IV was seen was over Tatooine. Here though it was different from before. We see the corvette get disabled and docked within mere minutes. During the fight we CAN assume that Vader was on the bridge and when the corvette docked he was on his way to the docking ramp (probalby first waiting to make sure not another surprise happens). As no time was to be wasted though the stormtroopers boarded the corvette as fast as possible.
So in essence.....the difference is a matter of time. In rogue one there was more time between disabling and boarding the ship so Vader successfully made his way towards the enemy ship at the same time as his troops. In a new hope there was not enough time for him to get from the bridge onto the enemy ship before his troops already boarded it (and they had to board it immediately.....letting an enemy ship sit within ones hangar even disabled could get the said enemies to get wrong ideas like overloading their reactor to take the star destroyer out with them, ...).
At least that is the impression I got from watching both films (never read the novels, so not 100% if the "time difference" also comes up in them or not).
According to the official novelisation, Vader actually boarded behind his troops when they entered the Profundity (as he did again when they boarded the Tantive IV), but proceeded alone when he caught a whiff of the Force, leading him toward the stolen transmission. His troops are heading toward the bridge but Vader decides to follow his own path which is where we pick up the action in the film.
Vader’s shuttle as Vader and his squad rode to the flagship. Vader felt fear then, too, vast and powerful and purer than that which emanated from the cruiser. When his vessel reached the flagship and his stormtroopers burned their way through the hull, he started toward the rebel bridge and then pivoted.
Perhaps instinct guided him. Perhaps something more. It did not occur to him to wonder. He sent his troops to continue on his prior path and moved on alone.
The corridor lights flickered while alarms blared. Trapped in the blood-red chamber of his helmet, Vader was troubled by neither. He attuned himself to emanations of panic and desperation and followed their trail. When he encountered rebels reaching for their blasters or dashing to seal blast doors, he drew his weapon and cut them down with unhurried strokes of his crimson blade.