When you compare two lovely things, use more beautiful, never beautifuler. Write: The second sunset was more beautiful than the first.
Beautifuler isn't accepted in standard English. You'd say This beach is more beautiful than the one we visited last year.
Even in casual speech, stick with more beautiful.
Choosing the wording by situation
Writing a postcard to your grandmother after a trip? Say This village is more beautiful than the photos suggested. That wording tells her you're weighing what you saw and picking this village over it.
Comparing two apartments in a message to your landlord? Write The bedroom is more beautiful than the living room. The longer form sounds natural because beautiful is a longer adjective, the kind that takes more instead of an -er ending.
Quoting your five-year-old, who said The rainbow is beautifuler!? Keep her words in quotes, then add your own correction: She said the rainbow was beautifuler. She meant more beautiful. The quote reports her wording; your sentence around it stays standard.
Comparing two sunsets you watched yourself? Try The second sunset was more beautiful than the first. Beautiful has more syllables than most short adjectives can handle, so it takes more for the comparative instead of an -er ending. The same goes for any sentence you write: when beautiful shows up between two things being weighed, more beautiful is the standard wording.
Quick check: which wording would you use, beautifuler or more beautiful? If you picked more beautiful, good result; that's the form standard English accepts. If you picked beautifuler, wrong result; it stays nonstandard. Revisit the examples above for usable sentences.
One exception to remember: beautifuler can show up only inside someone else's quoted words, where the writer records the speaker's own choice of wording. In any sentence you compose yourself, the standard comparative is more beautiful.
The one qualifier that changes the decision
Whether beautifuler works depends on whose voice your sentence carries. When you're quoting someone else's words, beautifuler can appear inside the quotation marks, because the quote simply reports what they said. When you're composing your own sentence, the decision is yours to make, and standard English takes more beautiful there. So a line like He calls the garden beautifuler than mine keeps his playful wording inside the quote while the sentence around it stays standard. If the sentence is yours from start to finish, write more beautiful.
Writing a joke where a character jokes about the word itself? Put it in the character's mouth, not yours: He calls the garden "beautifuler" than mine. The quoted word reports his playful wording, and your sentence around it stays standard.
Quoting someone else's playful or nonstandard wording? Keep their words as a report: My niece insists the puppy is beautifuler than the cat. Their wording sits inside your standard sentence, so the oddity belongs to the quote. The moment you're weighing two things in your own voice, the comparison is yours, and it takes the longer form: this view is more beautiful than the one from the trailhead.