If we stick to situations where special relativity is applicable, then we have no way to directly measure difference between time passed on earth and on spaceship, as their clocks can be synchronized only once (when they are in the same place). Thus it has no meaning to question where time goes slower.
What they will see is different question. When spaceship goes away from earth astronauts will see that processes on earth take longer than usual (simply from Doppler's effect with relativistic corrections), and so do earthlings. When spaceship goes toward earth, astronauts see that processes on earth go faster than usual.
Edit: Sorry for very tangential post.
Are you saying your argument is true with the strict application of only SR or that in is true in reality?
I would say it can not be true in reality because muons and other particles take a measurably longer amount of time to decay as their speed increases.
It has been suggested that animals have less subjective experience than people. For example, it would be possible to have an animal that counts as half a human for the purposes of morality. This is an argument as to why that may be the case.
If you're moving away from Earth at 87% of the speed of light, time dilation would make it look like time on Earth is passing half as fast. From your point of reference, everyone will live twice as long. This obviously won't change the number of life years they live. You can't double the amount of good in the world just by moving at 87% the speed of light. It's possible that there's just a preferred point of reference, and everything is based on people's speed relative to that, but I doubt it.
No consider if their brains were slowed down a different way. Suppose you uploaded someone, and made the simulation run at half speed. Would they experience a life twice as long? This seems to be just slowing it down a different way. I doubt it would change the total amount experienced.
If that's true, it means that sentience isn't something you either have or don't have. There can be varying amounts of it. Also, someone whose brain has been slowed down would be less intelligent by most measures, so this is some evidence that subjective experience correlates with intelligence.
Edit: replaced "sentience" with the more accurate "subjective experience".