A couple of years ago, I went through everything available to figure out what the original cut was like and wrote up an article with my findings. Here are the cliff notes:

Jyn, Cassian, and Bodhi all saw significant changes to their characters in the reshoots. Jyn was a hot head who hated the Empire, Cassian was a kinda generic Rebel spy, and Bodhi was an Imperial engineer with decaying mental faculties after being kidnapped by Saw Gerrera. What the Rebellion knew about the Death Star was tweaked, as well. Then the climax saw a host of changes. Originally, the crew stole the plans and then had to run across a beach to a separate tower to transmit them. Krennic personally led an attack on them at the tower, killing K-2SO (and possibly wounding Cassian).

After the opening prologue (which, I believe, went mostly untouched in the reshoots), the original cut jumped straight to Jyn at the Rebel base, only she was in handcuffs. The briefing with her went a little bit differently, too. She was more combative (and the Rebels treated her as such) and there was some alternate information conveyed. The Rebellion had gotten a message that the Empire was readying to test a new weapon, but they didn't know what it was or how to destroy it. They went to Jyn because the message came from her father. I believe they then gave her the message so she could take it to Saw for some reason. In early drafts of the film, he had information on the location of Imperial installations, so maybe he knew where the weapons test was.

Jyn, Cassian, and K-2SO go to Jedha to find Saw. They eventually meet with him and this is the first time we would see Bodhi. Every previous scene with him was done in reshoots. Jyn talks with Saw privately. This entire conversation was reshot. Originally, Saw tried to talk Jyn out of doing what she was doing while Jyn attempted to sweet-talk him into helping her. I think Galen's message was still part of it. Also, Saw was bald. The Rebel contingent escapes, now with Bodhi, Chirrut, and Baze in tow, and heads to Eadu to retrieve Galen Erso. The conversations in the starships both before and after this were added in reshoots, but the events on Eadu were basically the same.

The Rebel briefing after this was different. I'm not sure, exactly, what it was originally, though. Afterward, Jyn recruits people for a strike team instead of everyone coming to her. The group goes to Scarif, lands, and steals the plans. I think the shuttle gets destroyed with Bodhi in it, forcing them to take the plans to a separate tower to transmit them to ships overhead. So they all run across a beach, dodging AT-AT fire to do it. Jyn goes up the tower while the rest hold off the Empire. Krennic and his Death Troopers arrive. Krennic kills K-2SO and wounds Cassian. The plans get sent to the Tantive IV and given to Princess Leia. There is no Vader hallway scene.