The Atari 600XL and Atari 800XL are the same computers. The major difference is the amount of RAM. Only 16 kB (but expandable) for the 600XL to 64 kB for the 800XL.
Because of the 64 kB of memory for the Atari 800XL, this was seen as the biggest competitor for the Commodore 64. The Atari XL-range is amongst the better selling computers from the early 80s.
Unique of the Atari 600XL/800XL is that they can show 256 colors on screen and can handle 4-voiced audio thanks to the POKEY-chip. However, using 4 channels will limit the amount of usable octaves.