Somebody asked me the difference between the two. A short answer is “not much.” They are mostly interchangeable. However, as a Japanese teacher, I need to explain it a bit more.

It is originally さびしい and written like 寂しい

寂しい  has an emotional meaning of “lonely,” “lonesome” or “sad” as well as a rather objective meaning of “desolate” “deserted” or “quiet.”

さびしい can be used for both, but さみしい is more often used for an emotional meaning such as  ともだちがいなくてさみしい (I’m lonely because I don’t have a friend.)

懐が寂しい (I have an empty purse) can be read as ふところがさびしい or ふところがさみしい. The former is more or less stating the fact but the latter has a slightly more “sad” nuance.