The Asteroid has a more aggressive shape and better weight. While both are well weighted, the Asteroid seems to have a bit more weight where it benefits the stability and spin time of the yoyo better, which in the case of 5A might be a bonus for you.
The PSG ain't no slacker, but it's more "sand glass" shape, it reduces a bit of the catch area, but not enough where it should be a major concern. I think the softer shape will be a bit more comfortable but the general weighting is what is the drawback on it.
Fortunately, I have both but I don't have either set up for 5A, nor do I have any interest in doing so at this point, but that can change as my abilities with 5A improve over time. I'm not that good at 5A. I do think that the Asteroid is the more well rounded and adaptable player over the PSG. I don't have any regrets over the PSG, I happen to like it. In general, I prefer the Asteroid over the PSG.
Now, regarding 1A, both are solid performers based on preferences. 5A has a few more requirements that assist a player in having better performance out of their yoyo. The PSG is a bit slower. The shape seems to catch more air and move slower. The Asteroid, as mentioned before, is more aggressive. The Asteroid plays faster and slices through the air easier. As far as stability and stable, they are as good as you can expect from stuff in the price range as the Protostar and Northstar, but with performance right up there along with them at a fraction of the price.
It sounds like you're planning to get both. Congratulations, I think you're going to like your decision. Through this, please do take the time to experiment and see which one works best for you for the styles you're working with.