What? Android lets websites vibrate your phone and launch the Play store without permission? That's insane. This is one of the reasons I will never have an android phone.
There's an HTML5 API for vibrating devices, including phones; this isn't necessarily an Android-specific problem, and there are legitimate reasons for browser content to use features like vibration. (It isn't implemented in Safari, but it apparently works in other browsers on iDevices.)
The Play store launching without permission I haven't seen, so I can't guess at.
I have an Android phone, and I've never seen anything like this.
Then again, I don't do a lot of web surfing on my phone, and when I do, I use Firefox with uBlock Origin. Smooth sailing here....
Does iPhone even allow you to use a different browser? That's why I would never own an iPhone: you're supposed to pay a ton of money for something you can't replace the battery on or upgrade the storage on, and then you're not even allowed to customize it in any way or use any alternative apps to the Apple ones.
The Play store launching without permission I haven't seen, so I can't guess at.