Starsoul Mode: Increases Starsoul faster, so you can Slipstream (jump 5% distance) faster. This is good for shortening the distance to your destination. It also has Slipstream Skim, which temporarily increases your total speed, so your ETA is shortened as long as you keep tapping.
Thruster Mode: Makes you accelerate faster at higher multipliers, as well as do critical boosts. This is good if you want to tap a lot to increase your speed, but need to let the game idle for a while
Resource Mode: Good for getting the drones, shuttle, and shuttle abilities at higher levels than the other two modes, so you can use more powerful abilities faster. It also lets you get drones faster so you can level up more modes faster as well.