To add a little more detail, the 600 is an ECS machine with a plain 68000 chip. The 1200 is an AGA machine with a 68020. A stock 600 comes with 1MB or RAM, the 1200 comes with 2MB.
Historically the 1200 was considered easier to expand since it has a dedicated accelerator slot. Accelerators for the 600 need to clip on top of the 68000 chip, which is a bit trickier, and there aren’t as many options for them although some clever ones have been made more recently.
I think the 1200 is the better all around machine, but the 600 can be solid when properly expanded and its small size is just so darn cute.
