Appleis stock is listed on the Nasdaq stock exchange. Which exchange lists a stock is normally a technical issue that effects only your broker, be it a brick-and-mortar based broker or an online firm. From a perception standpoint, the NYSE and the Nasdaq have the most prestige associated with them, and many companies prefer or hope to have their stocks listed on one of those exchanges. Changes in regulatory issues have allowed exchanges to sell stocks listed at other exchanges, and the AmEx stock exchange, a competitor to the Nasdaq and the NYSE, announced that it is now trading shares of Apple.
The end result for most investors and stock traders will likely be limited to ancillary effects. With the AmEx and Nasdaq both offering Appleis stock, it is possible that exchange fees to brokers could be lowered, or new services offered to those brokers, and those changes might roll downhill to the consumer. In other words, the effects of competition between the exchanges might, or might not, have a net impact on the consumer, but nothing should immediately change with existing accounts and trading.