I treat all numbers differently, but for the first 4 bars I'll usually be listening to the whole number.
If I get past that point then I can focus on the rhythm, the music or the words depending on which one is strongest and catches my attention.
If the words are particularly strong, as per Dylan, Chuck Berry, Joni Mitchell etc, then the music might come a distant second. In some numbers the bass line will be the only interest, in others I'll not listen to the bass at all. I'll always listen to the drummer though.