Although a little fiddly on the iPhone (perfectly fine on the bigger iPad) I prefer using the browser as it maintains all the site specific functionality. But that's just a matter of personal preference - we're all free to choose!
But on the subject of being pestered by popups to install the Tapatalk app I used to get that, but haven't seen it for a long time on pinballinfo.com (I still see it on other forums). I tried logging out, clearing cookies and even using "Private" mode. Strange, huh?