The answer to that really depends which other mods you plan on using it with. Don't be put off by the "beta" tag, neither version is "scary" to use, it's not going to crash on you the whole time or corrupt your world.
GC2.0.14 latest version (2.0.14.1094) is pretty stable. There are some known incompatible mods which are listed in a sticky in the Support area of this forum. There are also some known bugs in it, maybe 20 or 30 total, which have been fixed in GC3 but left in GC2 because each one is small and not game-breaking. The worst of them is probably that if the player uses a Schematic in a NASA workbench, and then the player dies, you might find that the NASA workbench "forgets" some of the Schematics it once knew - so it's best not to put your Tier 2 Rocket Schematic into the workbench until you have the materials to make the T2 rocket.
GC3, even in beta, is
more stable than GC2 for all the things which GC2 can do (because those bugs in GC2, including the Schematics one, are fixed). But some of the new features in GC3 still have kinks, and there are a few visual bugs mostly minor. One big issue is that players can't visit other player's space stations in GC3 yet. This should give you some idea
https://github.com/micdoodle8/Galacticraft/issues/791.
If you're making a modpack, GC3 may have undiscovered issues with the 1.7.10 versions of some other mods, that is something still being worked out and you would need to figure for yourself the best mods to use or look around and see which mods other players have working stable with GC3.
Most importantly, if bugs or mod incompatibilities are found in GC3, we will be fixing them, though it may take us a few days or weeks to do. So if you're planning on playing your world for a long time, like 1 month +, I would pick GC3.