My galaxy s2 is currently set to the three.co.uk
Apn what would the difference be if I set the apn to 3internet?

They wouldn't block anything they would deem "inappropiate", for one thing...

Your device would be assigned its own public IP rather than being behind a NAT.

This would mean that your phone would 'wake up' every time something attempted to connect to that IP. This happens more than you might think, so would adversely affect battery life.

I currently tether my,s2 to the ps3 and get strict NAT on every game would changing the APN make the NAT open?

Depends on how the s2 handles it - the ps3 would still be behind a NAT created by the s2. Why not give it a try?