Parrot has an install option. If you're running it live, it's generally considered more secure, it's naturally going to run slower than it will run if it's installed. However, there's a finite value for security and you're probably (nothing personal) not all that 'rich' a target. Unless you're keeping nation-state secrets, you need to decide how much security is worth the effort.
At one end, there's zero security - which is just plain silly but we're expressing it for completeness.
At the other end, there's complete security - which means not using a computer at all.
Somewhere between those two extremes is where you need to pick a spot. Installing the OS will make it run much faster and not alter the security all that much so long as you continue to keep security in mind.