The answer is no.
The question of Apple Pay vs PayPal is an interesting one because each service means something different right now. Apple Pay, by being associated with Apple, attracts high value customers. Apple is a premium brand. Since its customers have signaled that they are willing to spend hundreds of dollars on devices, they are likely to do the same for other goods and experiences.
PayPal, on the other hand, is an older solution but one that is known for instilling trust between buyers and sellers. PayPal Buyer Protection protects buyers while PayPal Seller Protection protects merchants. These guarantees go a long way toward encouraging liquidity between buyers and sellers on its platform, and have led PayPal to be one of the dominant payment wallets.
Since Apple does not release Apple Pay adoption numbers, it’s hard to compare it to PayPal right now, besides knowing that it is growing very quickly. If Apple dedicates serious resources to Apple Pay and is able to build a higher level of trust than PayPal has, then Apple Pay could win.
Keep in mind the fact that Apple is focused on selling iPhones while PayPal is primarily focused on payments. PayPal only makes money when more transactions flow through its platform, while Apple is not solely reliant on Apple Pay succeeding to continue achieving unprecedented growth. Business models drive focus and one can often correlate the likelihood of a product’s success to how critical it is to the company's business. Here, PayPal has the advantage, but I would not count Apple Pay out. If Apple makes it a priority it could very well give PayPal a run for its money.