Well... I've read The Hobbit, LotR, The Silmarillion, each several times. Have also read The Unfinished Tales, though it's been some years since I read it as a whole (rather than bits and pieces), and have read The History of Middle-earth, as well as the things published (in America) as The Tolkien Reader (several times for that, as well, once for the 12-volume HoME). Have enjoyed them all, found each fascinating for differing reasons, and found the HoME at times very challenging, and full of surprises as well. Read the Letters a looong time ago (due for a reread as soon as my replacement copy shows up -- my original disappeared some years ago).
Answer -- yes, they all add to my understanding and appreciation of his world, his work, and the concerns that drove them, and my appreciation of his artistry. While I've always enjoyed LotR more than The Hobbit (which had a bit too much of a "speaking-down-to" tone for my taste), I enjoy both, and the other works have added tremendously to the levels which I can enjoy them on. The HoME also answers some questions I'd long had about, for example, the history of Old Man Willow, while posing new questions; it also creates several new frames within which to see LotR and The Hobbit, both artistically and philosophically.
As for what made differences... oooph! That's a tall order! Too much to go into at one go. Suffice to say that it makes it much clearer that what may appear a flaw in the book that we had originally often is actually there because that book was a part of a much, much larger whole, that I appreciate (even when I disagree with) so many things about his world that I either didn't particularly care for, missed, or felt disappointed in before, and have a much higher regard for Tolkien as a writer and artist than I had before (and I had a fairly good opinion of his work to begin with).