While I understand that real estate is very limited on a smartphone, one element of almost all modern day browsers that I have come to dislike is the top panel that keeps appearing and disappearing.
It is fairly common to have the top panel disappear when we scroll down a page. To go to another website, we need to pull down the page, to make the top panel appear once again, allowing us to type the new URL. I do not like this behavior, as the content keeps moving up and down, depending on the action performed.
Another grouse I have against smartphone based browsers is that they do not have proper back buttons and most depend on the ‘back’ button of the smartphone. Sometimes, this experience is not very friendly because I end up pressing the back button multiple times and I end up going back two or three pages backwards in history.