I'd say both builds would get you over the 60fps mark, and really that's all you need.
most people's monitors run at 60hz, so if your generating more then 60 frames per sec then those extra frames are pretty much discarded.

as for recording, i'd say switch out the CPU for a faster one. (not to start an AMD vs Intel discussion but..) from my experience, you should probably go for an intel chip. builds that involve Gaming only usually run AMD and do great, but builds that involve any sort of multitasking (recording/playing for example) usually run Intel. unfortunately, the multitasking bit comes with more cost associated with it.

furthermore, if you put the same AMD cpu and Ram into both builds then it wont matter what build you end up going with as you'll get the Same minecraft FPS on both. the reason is because minecraft is more Ram/CPU intensive then it is GPU intensive. Both GPUs will be able to run minecraft at almost any FPS you want (unless you use shaders) but it's the ram speed/Cpu speed that really matter with this game.

and lastly, these are benchmarks from my computer if your interested
my build: http://pcpartpicker.com/p/Q3yxt6
On max settings (with render dis 16): http://postimg.org/image/5ei6y5zoz/
On low settings: http://postimg.org/image/7qmbsuxep/

Those two builds aren't too bad (with the second build being pretty decent for the price), but you can get some better parts for that price range.

What's your maximum budget?

*Waits for a PC builder to say redirect you to a different build*