Doesn't seem to be widely known, but we've already reached "Peak child"
Well worth a look.
Seems we don't need to resort to any "population control" - but rather - to raise living standards world wide, and the population may just sort itself out.
Population still rising but only because people are living longer now than they ever used to and life expectancy especially in poorer countries continues to rise. May well reach a peak later this century and level off and slowly go down.
And - even 10 billion people - well the world is way under utilized in a way.
It's so much easier to build a new habitat in a desert here on Earth, or to reverse desertification - that it just doesn't make sense to go to another planet with this as the motivation.
We can breath the air - you can go outside and repair your desert greenhouse or habitat without a spacesuit, don't have to make all your own air to breath, or cover it with meters thick layers of ionization shielding - or build your habitat like a tank to hold in 10 tons per square meter of air pressure outwards. I think that it will always be easier to build a small habitat in a desert than to build a habitat for say a dozen people in outer space
Even really large space habitats like Stanford Toruses - may be easier to maintain per person - still- would be easier to build as floating Buckminster Fuller "cloud nine" type habitats in our atmosphere - a lot lighter - and easier to maintain, and cost far less to build.
So - my answer is neither. Focus on saving our planet - and on raising the standard of living of everyone world wide. Use insights from space settlement ideas to help the Earth. If it turns out to be worth doing, build solar power satellites and such like in space to bring energy to Earth.
And our population will sort itself out here on Earth.