In a 3-Piece Band: Bass or Drum?

Kinda off-topic of audio, but:
In a 3-instrument ensemble, which one whose absence will be less noticed: bass or drum?
There are some 3-piece ensemble that work well without drum, such as Nat King Cole Trio, copied by Diana Krall Trio (piano, guitar, bass). Patricia Barber's sometimes use only piano, bass, drum. I guess on a rock group, guitar, bass, and drum work well.
Looking at these combinations, bass is more than drum for a band to be musically 'complete'.
What do you think?
It's not so much the instruments themselves, but the role they play. For instance, a bass typically provides harmonic underpinning and rhythm. Organ pedals, tuba, piano and guitar can be readily substituted. For most groups you want an instrument for chords/harmony, a solo instrument for melody and some kind of rhythmic element. Good keyboard players can do all three at once. Great guitarist can also do the same. In groups it really depends on what you're trying to do as to which instrument does what.

BTW, Nat Cole dropped the drums to get a more elegant sound. He was trying to get away from jazz as a dance music.
Nice reply by Onhwy61.

Any combination of instruments can work given the right players, and the appropriate musical style.

However, I have yet to hear a rock band without drums, although I have heard a few rock bands with only two of which was drums (i.e. The White Stripes).

Jazz is another story.