The first one had no zombies. I played RE2 to the point of achieving all S ranks on all four difficulty settings. I probably put over 200 hours into that game.
The first one isn't bad, but it only had those creatures that mutated into monsters. No zombies. I only played the first one two times. Once on 3DS, then I bought it again for the PS3 for a bigger screen experience.
R2 is definitely the better buy, better story, better characters, everything.
I didn't necessarily like Natalia's part in the game. She wasn't really a "partner". She was the only thing I really didn't like in RE2. I also think they took away the partner having an actual gun away for the horror element part. It's scarier when you are basically going "solo" with no back-up.