The Gospels are no different than any other type of historic document. How do we know any of them are true?
Well, one thing you consider is how many authors wrote about something, and how closely their accounts agree (you’d be surprised how many times they don’t). To have as many as four different authors write about the same events is actually pretty uncommon in ancient texts - we’re lucky to get two. The Gospels don’t agree on every detail, but they’re close enough to be considered in very high agreement.
Another thing to consider is authorship. Eyewitnesses are best, and people close to eyewitnesses are acceptable. The Gospels were written by one eyewitness (John). Matthew was probably not the Apostle, but he was a Jew and may have known Jesus personally. Mark and Luke were gentiles and probably did not know Jesus, but they were close to people who did.
There has always been a science called “textual criticism” which analyzes ancient texts by comparing them to other contemporary texts. It analyzes how often certain words are used, and sentence structure, and “slang” and such. We can usually date the text very closely (within a decade) and tell a lot about the author’s background and education. In modern times, thanks to computers, we can feed in thousands of ancient texts to crunch the numbers to get unprecedented insight. We have run such an analysis on the Gospel texts and they check out very well.
These are the same criteria we would apply to any ancient text. When applied to the Gospels, the results are very favorable.
The Book of Mormon, on the other hand, came from “golden tablets” that Joseph Smith found in the woods. Nobody except Joseph Smith ever saw them (or was it dictated by Michael?). They were written in “New Egyptian,” a language otherwise unknown. We have only Smith’s word that the book accurately reflects the source. We have a single source, with no way to corroborate the text. Textual criticism tells us the book is the work of a single author, but we cannot date it because we lack the original text (the English translation, of course, dates to Smith’s day, and shows no syntactical influence from the New Egyptian source).