The Sorrows of Young Werther is an epistolary novel. How would the story be different if it were told from a different point of view?
Epistolary novels have certain limitations and advantages; the advantage is the person speaking (often the protagonist, but by no means always) can say exactly what he or she means. That person's thoughts and desires can be expressed directly by them, in the thoughtful and planned way that people often choose when describing things in a letter. This, of course, leads to a disadvantage -- if the person writing the letter is mistaken, deliberately deceitful, or simply unaware of some of the action of the novel, they cannot effectively (or believably) describe it. Also, the ability of the author to describe (or use literary devices) is limited by the abilities of the person ostensibly writing the "letter". The action of epistolary novels is often slower, too, and often limited as to length -- a very long novel of letters would be impracticable and would strain the readers' ability to suspend disbelief. Also, some actions that the protagonist cannot describe (such as Werther's suicide) have to be supplied by someone else; so the contrivance of other letter writers must be worked believably into the story.
The Sorrows of Young Werther is a short novel, and masterfully written, so the advantages are generally maximized while the disadvantages are minimized. Werther is extremely emotional and volatile, and his letters reflect that. If the novel had been written from Lotte's perspective (or even Albert's) it would be a very different story. We would know about Werther's actions and words, but not necessarily every single emotion he has, or their extremity. We would not be able to fully understand, also, the path that let Werther to suicide.
Written from Lotte's point of view the novel could be almost comic (which it could never be from Werther's perspective). She is comfortably promised to another man, and then Werther comes into her life with such extreme passion and inability to listen to reason that he affects everyone around him (usually negatively). His inability to accept that Lotte cannot (or will not -- and that question would be answered once and for all if Lotte had written the letters that became this novel!) marry him, and his conviction that his state of mind is somehow defensible, could be mocked by another letter writer. It could be written as tragic, too, or simply as a story of a troubled young man. It would not be the florid emotion-poem that Werther is -- it would be an entirely different story.