Performance and Long Range have the same battery, but the Performance version has iconel contactors and pyro fuses (1,760 Amps instead of 1500(?) Amps ) and the wiring to support the extra current. Performance cars have larger rear motors and inverters. The Ludicrous option (now) is just a software upgrade that can be applied to any Performance car. Other than that, the brakes as you mentioned, a spoiler and possibly some suspension tweaks.
Accurate to the best of my knowledge, but this info is hard to definitively find and there were changes with the latest Raven release.