For best finish remove the old tiles, with a hammer and chisel! What happens around door jambs and switches etc two tiles thick? Not a good finish, besides it's a great way to vent your frustrations! It's a job I've done a couple of times, I enjoyed the destruction!
Hi, I would go along with nungate on this one. Once you have got the first couple of tiles off the rest usually come of reasonably easily. Just make sure to wear eye protection and put cloth on floor before you start as this will make picking up the bits much easier.