Why are NOR flashes still used when NAND flashes have a bigger size?
It's not so much that NAND is not reliable (although it is less reliable), it's the fact that they are different sorts of memory in how they are accessed and the differences in speed of read/write; they are therefore useful for different applications.

NOR's main advantage is that it is random access, which makes it possible to use it to run code. It has a full address and data bus, so you can address any location and read from/write to immediately (writing assumes the address is empty of course). 

You read/write NAND by setting up the address through its small I/O interface then reading or writing data with the address auto incrementing with each read or write. This makes it good for writing or reading streams of data or files. Write speed for NAND is faster than NOR. When you're writing images on a camera, for example,  that fast write speed is especially useful. NAND's higher density is, of course, better for applications such as storing data. 

Edit: after Marcus' question. 

There is a reason for this access because of the way the MOSFETs are physically organised in the IC. To borrow a little from Wikipedia:


  In NOR flash, each cell has one end connected directly to ground, and
  the other end connected directly to a bit line. This arrangement is
  called "NOR flash" because it acts like a NOR gate.


The fact that each cell has one end connected to a bit line means they (and so each bit) can be accessed randomly. 


  NAND flash also uses floating-gate transistors, but they are connected
  in a way that resembles a NAND gate: several transistors are connected
  in series, and the bit line is pulled low only if all the word lines
  are pulled high (above the transistors' VT).


This means that every bit in the word has to be accessed at the same time.