Color me curious, what was wrong with the 1st that the second completely replaced it?
In my opinion nothing was wrong with it, I think it was mostly a matter of a change of ideas. Some for the better some not.
EDIT - You know what, it wasn't even a matter of change for better or not. It was just changes. The two aren't really compatible, but very similar, if you follow. More closely related than HG to B2. Though HG1 is maybe closer to B2 than HG2.
The character gen section didn't change at all, just the ship construction and combat.
What are some of the good bits? Cash is tight, like to have a good reason before I pencil it into the budget.
Let's see, a quick off the top of my head and skim...
Streamlining was more Book 2 methodology, no "partial streamlining".
Ability (and rules) for importing higher tech to build ships above local TL
Different drop tank rules
Different drive percentage tables
EDIT - oops, wherein I also meant to mention that Jump Drives don't need Powerplants
Different weapon factor calculations
Different armor calculations
Computers only up to model/7 (EDIT - and as noted by Mike below - Fib
and Bis for the full range)
Medical crew section (I'm convinced it was dropped by accident)
A nice summary of items for inclusion, many subsumed in the stateroom tonnage and cost (sickbays and... too many to mention here in the time I have)
Some interesting differences in design reflecting 1st printing of LBB1-3, like the Jump Governor.
Planetary bombardment rules using missile magazines and bays.
...I'll leave it to you to decide which are the "good" bits