As far as being immersive, it all depends.
Take a web site, like this one. If you only care about reading and responding to this thread, there is so much wasted space. I am writing the response right now using my MacBook Pro 15" connected to a 27" 4K display. The part of the screen I care about could easily handled by the 4 Mini. In a way doing this on a Mini is better (except for the typing part, but that is another story) because as I click on the part that I care about on the Mini 4, I can zoom in on what I need and get rid of all the distraction. Having a bigger screen is not really enhancing the experience here.
My point is that if the content you want is formatted efficiently, then most of the time a 4 Mini is wonderful. Sure, there are exception like watching a movie or a large format magazine. But reading is not one of those. Text should be formatted in lines that are not too wide so that one can read without changing moving one's head, and the Mini 4 is wide enough in portrait orientation to accommodate ergonomically formatted pages, the way all print publications are.
I am a software developer, and what I see is that more and more contents are formatted intelligently nowadays to accommodate smaller screens like iPhone 6, 6 Plus well, let alone a larger screen like the Mini 4.
When the content fits, the 4 Mini is a breath of fresh air compared to the Air/Air 2 in term of handling.
When I had to decide between the Mini and the Air 1 a few years ago, I went with the Air 1 because I felt that I would rather be safe than sorry. Now that I have my Air 1, I no longer need to be safe, and knowing that how cumbersome the Air 1 was for reading, I decided to try the Mini 4. This is the sort of thing that you have to try for yourself. My experience is that the Mini 4 made a huge difference in term of reading ergonomic.
Back to the topic of being more immersive, I never am interested in watching a movie on a portable device. If I do, I imagine I would prefer my 15" laptop to either my iPad Air 1 or the Mini. Perhaps the iPad Pro would be on the top of my list to watch movie on. My point is that it seems the Air and the Mini 4 both have very small screens for movies, so it's a compromise to start with either way. I am not sure I would pick one over the other for movie and disregard other attributes. It's like picking a wagon over a hatchback when your need is a van.