I guess the only appeal of third-party browsers on iOS is synchronization with their desktop counterparts. Maybe ad-blocking if the capability is offered (I'm not so sure about this one)

The main draw is sync with other browsers. That part actually works pretty well; You can easily send web pages from your desktop to your phone, or vice versa. History, bookmarks, etc all sync, giving the user a more homogenous experience. If I look something up on my desktop, I can quickly return to it while using my phone.

Basically, since all browsers were required to use WebKit, the only real difference between the browsers was which UI and sync method you preferred.