The Allen-Bradley series 1764 number refers to the Micrologix 1500 programmable logic controllers. (I find no references to the number 1764-L64). The Micrologix 1500 processors available, according to the user manual, are the 1764-LSP and the 1764-LRP Enhanced with RS-232 port. The Micrologix 1500 is a low-to middle-range PLC in terms of memory and I/O points. The Micrologix 1500 has a maximum 16 Kbytes of memory and only 28 points (16 inputs and 12 outputs) of embedded I/O, but up to 16 additional Compact I/O expansion modules may be added.
The 1756 ControlLogix controller series is a mid-to-high range PLC, and "provides a scalable controller solution that is capable of addressing a large amount of I/O points". The 1756-L63 model has 8196 Kbytes of user memory, 478 Kb of I/O memory, 64 Megabytes of Compact Flash non-volitile memory, and uses 3.6 watts of power.
The ControlLogix controller can be placed into any slot of a ControlLogix I/O chassis and multiple controllers can be installed in the same chassis. Multiple controllers in the same chassis communicate with each other over the backplane (just as controllers can communicate over networks) but operate independently.