Dual GPS and Galileo receivers will be required. They are already on sale now (for marine and land use at least, I don't think aviaiton sets are available yet).
Galileo is more accurate. It's a new system whereas GPS dates from the 80s. The system can't develope much when the original satellites are still in use. Although GPS Block 2 satellites are flying and Block 3 are coming soon, they are still hampered by the limitations of the original system. Galileo achieves 1m accuracy in it's basic mode. It's also much faster to aquire and compute a position.
GPS has a problem in that the programme of replacing satelites is behind schedule. Recently, the US Government accountability office warned that full coverage may be lost in the near future due to this.