“A similar hat to Jane” vs “A hat similar to Jane’s”

Jane is obviously not a hat, so it’s hardly confusing. I would analyse it as a rather extreme ellipsis in which the repeated noun and verb are both removed.

John always wears a similar hat to [the hat which] Jane [wears].

Whether I would write that, I’m not sure. Speech tends to be more compressed than written language, and it’s possible to take more time over being careful when writing. I might write Jane’s.

It isn't just BrE speakers who produce this kind of unclear English. AmE speakers have been doing it for decades—and probably centuries as well. It's not fit for formal writing simply because it's nonsense.

"A similar hat to Jane" isn't the same as "a hat similar to Jane": the latter has meaning and would normally be found in things like Ionesco plays and Oliver Sacks books (The Man Who Mistook His Wife for a Hat: and Other Clinical Tales), but the former is syntactically skewed. The word order (for some of us, at least, word order matters) turns the phrase into a semantic vacuum. But...someone will stand up and say that it's perfectly normal where they live and that everyone there understands it to mean that the similar hat is very much like the hat that Jane has and in fact means a hat similar to Jane's, which is what it should be.

BrE speakers often use "to" when making comparative statements: "A is different to B"; AmE speakers tend to use "than" and "from": "A is different {than / from} B". Nothing remarkable there.

Then, of course, there are sentences that declare that Jane and Jayne are wearing the same dress or that Jayne's dress is identical to Jane: "I was so humiliated at the party! Jayne came in wearing the same dress as {I was wearing / me}!" If it was indeed the same dress that I [Jane] was wearing, then Jane must have suddenly been in her undies when Jayne walked in, but if it was the same dress as me [Jane], then Jane must have been draped around Jayne instead of standing in the room and feeling humiliated.

And so, you see, the grammar gods are dead and probably only apocryphal or mythical anyway. People will say what they want to say and will defend their right to say it to the death, regardless of what it sounds like or what it may seem to mean to others. As long as they and their listeners/readers know what it means, what does it matter? It's no different from reading Dickens's or George Eliot's or Mark Twain's or William Faulkner's dialect dialogue, or Beowulf in the original without a glossary: you either get it or you don't. If you do, you're amused; if you don't, you're annoyed.