The '....Royal.....' is meaningless w.r.t. the quality of training. You're no more, and no less, likely to get good training at a royal aero club than at any other aero club or flying school. The 'Royal' denotes that the organisation holds a royal charter to engage in some purpose.
To quote from Wikipedia (since it happened to be convenient):
A charter is a document bestowing certain rights on a town, city, university or institution. The term derives from a root word meaning "paper".
As John Fiske described in his 1890 treatise on the Origin of Civil Government in the United States:
The word "charter" originally meant simply a paper or written document, and it was often applied to deeds for the transfer of real estate. In contracts of such importance papers or parchment documents were drawn up and carefully preserved as irrefragable evidences of the transaction. And so, in quite significant phrase the towns zealously guarded their charters as the "title-deeds of their liberties."
After a while the word charter was applied in England to a particular document which specified certain important concessions forcibly wrung by the people from a most unwilling sovereign. This document was called Magna Charta, or the "Great Charter," signed at Runnymede, June 15, 1215, by John, king of England.
Charters were issued in medieval times by Royal decree, perhaps giving a particular town the right to hold a weekly market, or to levy a toll on a road or bridge.
A charter is a legally binding document incorporating an organization or institution and specifying its purpose, remit or bylaws. Organisations such as the Institution of Civil Engineers in the UK is chartered to maintain and advance the science and practice of civil engineering in the UK, and by this charter has the right to regulate the business of civil engineering in the UK; this gives rise to a status of a chartered engineer - one who satisfies the requirements of the charter holding organisation.