First off the Linux and Mac ports are superb. Gone are the frame skips and load issues of the past. One amazing feature Rebirth sports is native controller support. I know some Isaac superfans are keyboard only but I do like playing it with a controller.
Rebirth also sports a new soundtrack and pixel art style. I think I prefer this to the original but if you like a more smoothed out style, there is an option for you.
I have only a few hours into Rebirth so I can't comment on the new content but I can say that the game feels more fair. I have mentioned this to some Isaac fans that don't agree but it's just an initial impression. I'll post more thoughts on Rebirth later so stay tuned.

I never played the original, but after seeing a Lets Play of Rebirth I decided to open up my Steam wallet and buy it.
I too am only a few hours into the game, but it has been a lot of fun. I like the controls a lot, but wish there were a way to know what items are before picking them up. I'm sure I'll figure them all out eventually, or I probably could find a wiki, but I think the intention in the game is to explore and not know what you're coming across, so I'll leave the wiki for later.