They are utterly different animals, so it depends on what you want from your game.
The LBB are terse, open-ended guidelines put together for a group of hobbyists who already enjoyed crafting their own worlds, rules, scenarios, etc. The "rules" were broad suggestions to get the juices flowing in the right direction for people who were already actively engaged in wildly creative individual endeavors, so that they might be able to get their head into fantasy gaming. The books are unclear in places, but this was most likely not an issue for readers, who probably spent 30 seconds or so trying to figure out any tough spots before just making their own ruling and getting on with play. For contemporary gamers, accustomed to A-Z, spit and polished, ready out of the box games with high production values, it will be frustratingly unclear and inchoate.
The RC (of which I am not generally a fan) came much later in the life of the hobby, when that A-Z, spit and polished, ready out of the box style was more standard. As a result, it's 305 pages of material covering everything from fledgling adventurers to world-shaking conquerors. To me, it is packed to the gills with unnecessary exposition, years of complicated rules piled on top of the simple system of earlier Dungeons & Dragons sets (which ruined the beauty of D&D vs. AD&D), and a plethora of material that I'll never use in my games since we top out around levels 12-14. The standard advantages touted by fans are 1) its completeness, and 2) its convenience. If you use a great deal of the material, those are most likely true, but as someone who uses well less than half of the rules found within and gets everything he needs from two slim softcovers, neither of those is terribly compelling to me. Honestly, I don't understand the rave reviews the RC gets. It's poorly edited and has blah artwork, as well (not that I'm forwarding the LBB as paragons of artistic endeavor, but with the adulation normally shown the RC, I was surprised at how uninspiring its art is). All of that said, if you don't have the time or inclination to pour into a campaign behind the scenes, and if you plan to run to high levels and want a solid rules framework to build your game on, it's probably the better choice for you.