The Binding of Isaac: Rebirth is the rightful heir to the first game. Including the original content of both the vanilla game and The Wrath of the Lamb DLC plus totally new content, the game is definitely better than the first installment.
The game is no more designed with Flash, thus it has no more problems of frame rate loss without apparent reasons. This also brought to the game a pixel art graphics which is nicely done, but not everyone might appreciate it. On the other hand this helped developing the game in a more free way, with more synergies and items in general. The soundtrack is also very good.

If you liked the first The Binding of Isaac you definitely need to buy this game.