At the time, the special effects were nothing short of astonishing. I can look at them now and see the flaws, but back then they were cutting edge. And it really is not suited for TV - any TV, no matter how large. It was made for the theater, and I can assure you that when the Mothership comes in in the theater, it really is an awe-inspiring thing.
There are particular scenes that just stand out as being particularly good scenes on their own. The bit with the flight controllers, with the technical talk and the over-lapping dialog is a classic of the type.
Obviously, I can’t forget I’ve seen the film and see it with your perspective. But I do think it’s in that class of films like Citizen Kane that need, and deserve, to be seen in a theater to fully appreciate. For a recent example, people who watched The Hurt Locker at home sometimes report being unimpressed. But when I saw it in a state-of-the-art theater with 4k projection, 11 channel sound and a bass shaker mounted under my seat, I walked out of the film literally stunned.
It’s hard to come up with a comparison, but with some films, seeing them at home on a TV instead of seeing them in a theater is like comparing masturbation to sex. Enjoyable enough, but nowhere near as satisfying.