I used an ATMega128 based board at the university, but i would like to buy my own arduino.
Initially i preferred the Uno, because it is newer, but some of the uno users (on the internet) said that Duemilanove is more reliable, and its easier to program. Is this true?
No, they are basically the same from a reliability and ease of programming point. The uno uses a small, faster baudrate bootloader, so uploads happen faster and there is a little more sketch memory space then the older board.
Can you describe whats the difference between them and help me which one should i buy?
Different bootloader, different USB serial converter chip.