Altera DE2 Board vs Altera NEEK Kit, which would you choose and why?

For learning purposes, I would go with the DE2. There's a wealth of resources across the internet for reference designs.

Here's a couple of examples:

http://people.ece.cornell.edu/land/courses/ece5760/

http://www.altera.com/education/univ/materials/digital_logic/tutorials/unv-tutorials.html

Here's a list of schools that use the DE2 and links to their pages:

http://www.terasic.com.tw/cgi-bin/page/archive.pl?language=english&categoryno=12&no=329

The NEEK board is suited towards developing with Nios II, and the reference designs you will find are geared towards this.

As you are learning about the potential about FPGAs, you would want to stick with implementing things in hardware. As for the memory issue pointed out by

matrixofdynamism, the DE2 board only uses SDRAM, not DDR.