Haven't played BS2 DC yet.
BS1 DC, aside from fixed bugs (especially the goat one), new characters' portraits and one or two additional puzzle/screen also has additional sections with Nico that happens in the same time as the main events of the game. Nico's chapters have few good puzzles and give you some backstory to Nico's life. While I enjoyed playing them, I think Nico's story breaks the pacing of the game. It's obvious that those sections weren't originally in the game and were added later thus affecting the experience. Take the beginning for example - the game doesn't start with the original intro (the clown attacking the restaurant) but instead you first have to play through Nico witnessing another murder a night before it; thus instead of starting with the big boom, the game starts with a slow investigation. On the plus side, at least you know that while George was globetrottering, Nico wasn't just sitting in her apartment doing nothing all the time.
Also, the change in artstyle (between old cut-scenes/dialog closeups and new cut-scenes/character portraits) can be a little jarring. As can be the difference in sound quality (Nico's sections have much higher quality sound samples than the original game and it's noticeable - especially when you compare Nico's voice in those new sections of the game and her in the original game).
However, I can still recommend playing it. After all, it's still the original BS1 with fixed bugs and additional puzzles. And if you already played the original one, those differences in storytelling won't affect you.
And if you're planning on playing them on smartphone or tablet, the interface is fantastic. Seriously, after playing Broken Sword 1 on my phone I'm amazed that there are so few adventure games on touch devices.
