NATS offers a much better chance of avoiding London as 90% of the trainees will end up doing Area control instead. In terms of training I have no idea what ANS are like, but being tower only will give you more flexibility to move elsewhere in the country. With my Area rating I'm stuck at Swanwick or Prestwick or the few countries abroad that allow non nationals, and have English as their main language, to work in air traffic.
ANS don't do the approach for Gatwick, that's done by NATS at Swanwick and I'm not sure about Edinburgh.