How does Ajita Kesakambali compare to the Buddha? DN 2 states:


  When this was said, Ajita Kesakambalin said to me, 'Great king, there is nothing given, nothing offered, nothing sacrificed. There is no
  fruit or result of good or bad actions. There is no this world, no
  other world, no mother, no father, no spontaneously reborn beings; no
  brahmans or contemplatives who, faring rightly and practicing rightly,
  proclaim this world and the other after having directly known and
  realized it for themselves. A person is a composite of four primary
  elements. At death, the earth (in the body) returns to and merges with
  the (external) earth-substance. The fire returns to and merges with
  the external fire-substance. The liquid returns to and merges with the
  external liquid-substance. The wind returns to and merges with the
  external wind-substance. The sense-faculties scatter into space. Four
  men, with the bier as the fifth, carry the corpse. Its eulogies are
  sounded only as far as the charnel ground. The bones turn
  pigeon-colored. The offerings end in ashes. Generosity is taught by
  idiots. The words of those who speak of existence after death are
  false, empty chatter. With the break-up of the body, the wise and the
  foolish alike are annihilated, destroyed. They do not exist after
  death.'


Ajita Kesakambali is similar to another wrong view, found in DN 1, namely:


  Herein, bhikkhus, a certain recluse or a brahmin asserts the following doctrine and view: ‘The self, good sir, has material form;
  it is composed of the four primary elements and originates from father
  and mother. Since this self, good sir, is annihilated and destroyed
  with the breakup of the body and does not exist after death, at this
  point the self is completely annihilated.’ In this way some proclaim
  the annihilation, destruction, and extermination of an existent
  being.


Now the Buddha taught extensively about the elements, such as in MN 115 &amp; MN 140. 

Or in MN 43, Sariputta mentions how the sense faculties are scattered at the termination of life, as follows:


  Yvāyaṃ, āvuso, mato kālaṅkato tassa kāyasaṅkhārā niruddhā paṭippassaddhā, vacīsaṅkhārā niruddhāniruddha paṭippassaddhā, cittasaṅkhārā niruddhā
  paṭippassaddhā, āyu parikkhīṇo, usmā vūpasantā, indriyāni
  paribhinnāni.
  
  In the case of the one who is dead, who has completed his time, his bodily fabrications have ceased &amp; subsided, his verbal fabrications
  ... his mental fabrications have ceased &amp; subsided, his vitality is
  exhausted, his heat subsided, &amp; his faculties are scattered.


How do the teachings of Ajita Kesakambali &amp; other annihilationists compare to those of the Buddha? What makes them different?
his mental fabrications have ceased &amp; subsided


This refers to the mental activity in this body. It doesn't mean that there's no next life after death, unless we are talking about an Arahanth. This is why having a good teacher is important. If someone with materialistic views try to interpret this sutta by himself, he might conclude that it all ends after death.