The distance depends on the interference in your flying area. If you're not happy with the distance, you could always add an antenna booster for about $100. That'll make your remote controller larger, so you'll then need to find a way to store the remote controller with that extra equipment attached -- or remove it each time when you're done flying.
I don't care for the P3S remote controller since it cannot hold a tablet as-is out of the box and it does not have all of the extra buttons. If you're planning on using a tablet with the P3S, then plan on spending another ~$40 to mod it so it can hold a tablet. At that point, it makes sense to get the P34K since it has a better remote controller along with the built in tablet holder.
As for rating them, I prefer the P3A (or P3P) since it has Lightbridge, GLONASS, a better remote controller, does not require switching the Wi-Fi connection each time I fly, and does not require mods to work around the shortcomings found in the P3S.
The P3S is by no means a bad choice though. It'll be perfect for flying up to a 1/2 mile in many locations.