Well, to be honest, they’re not really all that similar. But sometimes, Morrissey has a certain turn of phrase that could easily fit within a Doors song sung by Jim Morrison. It goes both ways, in fact. There’s quite a few lyrics on The Doors’ albums that would have sounded right at home on a Smiths record.
Just for fun, I’ve explored this idea in a new “game show” style video. Here’s “Morrissey Vs. Morrison”: