I've seen a lot of comparisons between the tw0 - haven't played the original, so here's what I've seen so far;

• Isaac is changed up a bit. In the original, he had no voice lines at all and was mostly silent... save the pained grunts and screams. Here, he speaks a lot and reacts more with the world.
• Characters are changed up a good bit as well, but not by much. The other members of the Kellion are a lot nicer and don't devolve into infighting that much compared to the original. One crewmember's death is completely different; not that much of a spoiler since in the original, he was just killed in the Necromorphs' intro - now, she (yes, emphasis on different gender) just lives a few minutes longer before being killed off in a different enemy type intro.
• Weapon upgrades were completely reworked, bringing them closer to later entries. There is one unique thing - you need to buy additional weapon upgrades to fully unlock upgrade maps.
• Space walks were changed as well, letting you use the jetpack from the second game onward.
• A much hated mission objective was completely changed, which some let's players like Jacksepticeye stated was for the better.
• There's much more exploration in the game now, letting the player freely return to past areas to explore for upgrade materials and supplies. The game also offers sidequests as well, again for unlocking vital supplies.

There are also new unlockables to the game as well. If you beat the game on the hardest difficulty (same as hard mode, but you're only allowed one save slot and dying deletes your file), you'll unlock the infinite-ammo super weapon from Dead Space 2 for use in later playthroughs. >!Yes, the foam finger returns.!< Also, the hardest difficulty adds a special objective to gather collectables to unlock a new ending.