I think it’s worth remembering Starling had around a year head start on Monzo with building the current account. And on top of that Monzo had built the prepaid product whilst building the current account.
With regards to Apple Pay, there are 3 components (that I know of) on the bank side that are needed for Apple Pay to be work. The first is with the payment network (Visa, MasterCard, AMEX etc), the second is with the bank, and the third is with the payment processor.
Obviously, Visa, MasterCard and AMEX have sorted their end out.
And obviously all banks need to integrate Apple Pay into their actual stack.
But with regards to the payment processor, Starling is outsourcing it’s payment processing to a third party, GPS (http://globalprocessing.net). GPS supports Apple Pay, so for Starling, there isn’t really any work to be done here. Monzo on the other hand, have decided to build their own payment processor. This is because of the frequent outages GPS have had (even quite recently), which still plague Starling.
As you can imagine, building a payment processor isn’t easy (the fact there are successful businesses setup to do just this, shows). And then on top of that: build Apple Pay into the payment processor.
It’s also worth noting that Apple’s agreements are usually very stringent, particularly around testing, and I imagine Apple requires Monzo to do enormous amounts of testing (particularly on the payment processor side, that Starling has skipped).
And all of this is assuming Monzo are even working on Apple Pay 
Monzo creating their own payment processor will only pay dividends in the future, as any further outages with GPS will not effect Monzo, but still effect GPS’s customers like Starling.