A properly designed web app will cache most of the necessary resources so you won't need to download it more than once unless it changes. It can even operate offline in some cases. Web apps can use some of the host devices but not all unless you convert it to a native app using PhoneGap or something similar. They are not as fast on iOS but this is because Apple chooses to make it that way, they want you to have to go through the App Store and pay the Apple tax.
The word 'properly' is the key here. Most front-end devs can't do anything without heavy frameworks and other libs. Techniques such as Single Page Apps are not very performant, at least not in the early frameworks.