(I'm disappointed there's virtually nothing around here about strategies for Ad Astra. So I'll just have to write it myself. If you guys like this, I might write on some other aspects of the game.)
At first glance I thought the game had 5 different colors playing from the same decks... but not quite. Each player can reach only 6 of the 8 systems with their own movement cards, the rules even say so, but the subtle thing is the 5 factions are playing different resource production cards. Each player can produce different combinations of resources. I really like this, because it means the game has factional differences but they're not blatant bonuses but part of the game mechanics.
I'm going to run-down what each faction's production cards mean for strategy.
Grey: Produce food/water means they can never produce BOTH food and water in the same turn themselves. As a result, Grey tends to be slower to build colonies and terraformers. Generally grey will lose out to other players in a race to build the most terraformers, and should emphasize other scoring strategies; most systems being the most obvious as it's the other side of the score terraformers/systems card. Also, because grey cannot produce the resources for a colony in 1 turn, grey tends to be the faction most reliant on trade.
Red and Blue: These players can produce all minerals in the same turn, making them similar. They tend to be fast at building ships and factories. They can also play the resources to make a colony in 1 turn. The red's energy/yellow mineral card makes yellow mineral valuable for building colonies, while the blue's energy/red mineral makes red mineral valuable for their faction. On the downside, those energy/mineral production cards tend to make these players move their ships less, and fully devellop the first system they move to.
Yellow and Green: These factions have energy and food or water production cards, making them similar. Yellow can produce water/energy, green can produce food/energy. This tends to make them expand systematically, as they can play energy+movement+movement to reach new systems in 1 turn, then the resources to make colonies the next turn. Also, the yellow faction's food/red mineral card makes red mineral less valuable to their faction for building colonies, while the green player's water/yellow mineral card makes yellow mineral less valuable for them.
One caveat to all this is that, in my experience, each player's first two planets (the homeworld and first planet they land on) makes a bigger difference than their faction's production differences, though the differences will shade which planets are desirable for each faction to colonize.