LBB2 starship combat is intended for miniatures movement on a table surface, or at least graph paper, and is geared towards ACS battles (Adventurer Class Ships). It has movement, computer program handling, and a simplified damage/build system including missiles, lasers and sand as primary weapons.
HG is geared towards building and operating large battle fleets filled with large ships and big exotic weapons. Combat is abstracted into short/long range, only range change maneuver, computer differences are simplified into a die mod, and weapon/defense interactions and therefore builds are more complex.
A companion piece to HG, TCS or Trillion Credit Squadron, handles rules for an abstracted space empire campaign version of HG.
A CT overview would be incomplete without mentioning Mayday, a board game version of maneuver that is more abstract then LBB2 but less then HG.
So, a lot of which system you choose depends on your entertainment goals.
Keep in mind you can handcraft what you want out of the base material. For instance in LBB2 many people forego the computer handling subgame and/or the hard maneuver aspects, choosing range bands like many later versions do.