Answer... its complicated.
How big consititues as tiny pieces of rock, in a galatic sense the earth already is a tiny piece of rock, but obviously thats not what you meant. But would boulders the size of buses be enough, that's definitely tiny compared to the earth, but not compared to gravel which is indeed tiny pieces of rock... so then so is sand in a sense. the smaller you make the pieces of rock the more work it takes to do so...
So option 1 is open to interpretation... but consider its a lot easier to break apart some rocks into smaller rocks then it is to split atoms, rocks are just simple molecules of atoms arranged in a specific way.
Why is this important you ask? simple, you want to split the planet in half, now if i were to assume you meant perfectly in half which for comedic purposes i will believe you did then that perfect cut will need to be so fine that it cuts atoms apart, which takes a huge amount more energy. and i mean huge, somewhere in the region of many many 0s ber atom, and there is not just a couple of atoms between one side of the planet and the other
Then of course consider that most of the earth isn't rock... its lava and other slightly warm things, so you would only need to break about the top 20km off before what you were dealing with wasn't rock anymore, so you couldn't break it into tiny pieces of something tis not, maybe globules of lava. doesn't have the same ring to it though really.
of course that is again probably not what you meant. but consider... The only way to split the planet in two and not have them recombine due to gravitational binding energy. is to do one of two things
- Split them in half and move one half into a completely different orbit where they will be unlikely to ever be drawn to each other again.
- Split them in half and spin both halves so they orbit a central point between them while orbiting the sun.
The fact that you didn't specify that the "tiny pieces of rocks" aren't allowed to eventually bind back together means that one the planet is destroyed the debris field would form similar to the asteroid belt, that may one day bind back together to make another planet. so the tiny rocks don't need to be moved all that much.
And moving all of the rock is going to be at least the same as breaking it apart. so probably option 2 would require more energy.
i just want to apologise in advance if any of this sounded sarcastic... it wasn't meant to be, I've had one of those weeks when i went and re-read all of XKCD again... i may be thinking in his writing style right now