This question comes up sometimes when people hear about the cash incentives offered by the DfES through the Institute of Physics in England. These incentives offer a bounty of up to £30K but they are subject to terms and conditions.
If you apply for the bursary, you will be required to make a written commitment to seek a teaching post in England. I know of nobody who has completed PGCE in England, picked up the bounty money and crossed the border. I am not sure that if you reneged on your commitment to teach in England, you would not be required to repay some or all of the bursary. A Scottish PGDE gives you guaranteed entry to the Teacher Induction Scheme that allows you to complete your probation in one year in a state school. There is nothing to prevent you from applying for GTCS registration after a few years teaching in England but be aware, you are likely to still need to complete a probationary period before gaining full registration status.
General observations are that although English PGCEs are every bit as valid as the Scottish PGDE, there are other routes into teaching in England. I believe that even the QTS is being abolished there as part of the academisation of all state schools. The Scottish stance is much more guarded: we insist on fully qualified and registered teachers, even in the independent sector. This is one of the reasons that Scottish qualified teachers are so highly regarded around the world.
(cross-posted from LinkedIn Teaching Physics in Scotland Group)