There are many apps that are bundled into iOS that are showing their age, and there are many alternatives on the App Store that offer a greater user experience, interface, features, and functionality. Take for example the Messages app. When the first iPhone came out this was the absolute best texting experience you could get! A threaded chat conversation that I can scroll through that offers a high level of polish to the UI was fantastic. But compared to what GroupMe and Facebook Messenger is doing, it is not up to snuff. You can't rename grouped messages (i.e. Family, Work Friends, etc.), the only media type that can be shared from the Messages app itself is either a photo or video (no location or audio), and the app doesn't even show a photo of the contact you are messaging on either the messages list view or the chat view. There are significant omissions that are being pointed out by more modernized and elegantly crafted alternatives and it doesn't stop at the Messages app.
These trends can be seen in the Mail app if you compare it to something like Sparrow or the upcoming Mailbox app. It is getting to a point where the paradigm shift that was the iPhone in 2007 compared to the dumbphones that preceded it is becoming increasingly similar to the better, faster, more featured apps compared to the stock iOS offering. Android on the other hand has a similar yet different problem.
There are many instances in which each mobile OS can present a case for remedying the issues that I have mentioned here, but until there is a solid solution for this upcoming / happening mobile OS shift, we're going to be left using "dumbsmartphones".