Biisi is slang, laulu is not.
Biisi is more often used to refer to pop-songs, you'd not hear an orchestral piece be called a "biisi". Laulu, like song, usually refers to music with vocals, while biisi does not necessarily have to refer to something with lyrics. Calling Darude's Sandstorm a "biisi" would work, but calling it a "laulu" would not.
According to the finnish etymological dictionary, biisi is from the the english word "piece". The finnish word for "piece" is "kappale" and can also be used to refer to a song, or in fact any "piece" of art, kinda like in english.