I voted no, because you didn't include a third option.
It is not overpopulated. The population does not *have* to be a problem. It could increase a hundredfold and it would still be something we can cope with. The only reason it's causing problems is because we allow it to; there are plenty of solutions and they don't require genocide to accomplish, we just don't currently appear have the global organization and drive to embrace them.
Where do you propose to get the resources for 700 billion people?
That's about 2200 sq ft of land area per person. How do you propose to grow enough food in such a small patch of land? Even if you add in the oceans you're still at less than 1/4 acre/person.
Note that indoor growing is *NOT* an option--while you could have any number of levels of plants growing under light the resulting world would be uninhabitable. Lets say we build structures to support double decker agriculture over the whole surface of the Earth. That will give 1/2 acre/person--tight but under greenhouse conditions it's possible. One layer can use sunlight, the other will have to use powered lights.
Unfortunately, I'm having no luck finding useful numbers for those lights so it's time to whip out an envelope: Sunlight at the Earth's surface is just under 1000 w/m^2. I'll be generous and figure you can halve this by lights that selectively emit the best frequencies--500 w/m^2.
Temperature goes at the 4th root of energy, we increased the energy by 50%, the temperature goes up by 10%. The average temperature of the Earth is 15C. Oops--you have to use an absolute scale, that's 288K. Increase that by 10% and you're talking a 28.8 (C and K use the same size degree) degree rise. That 15C average goes up to almost 44C--111F for us non-metric types.
The only way we could actually live in such a world is to have an air conditioned and completely sealed environment. Those air conditioners will use a *LOT* of energy, it's going to be even hotter outside--your survival time would be no more than a few minutes outside.
Furthermore, you'll need to bottle up the Earth's water supply or you'll end up with a thermal runaway like Venus. Your air conditioner radiators will be at red heat and you'll have to build everything like a deep-diving submarine. (And note that the sun won't be getting through, everything will be under lights, even more power.)
Larry Niven got it right when he figured the Puppeteers would have to move their homeworld out into interstellar space to keep it habitable.