The t (t) over barb (b) over bar production is a dominant background for th
e SM and MSSM Higgs search in the associated production t (t) over barH wit
h H --> b. This paper presents a comparison for the background rates obtain
ed with the Monte Carlo generators: PYTHIA5.7 and CompHEP. In the case of P
YTHIA the tt production is generated in the hard process and the remaining
two b-quarks are obtained from the partonic cascade. In the case of CompHEP
an exact matrix element for t (t) over barb (b) over bar production is use
d. A detailed comparison of the cross-sections and the expected acceptances
is shown for several steps of the selection used for the extraction of the
Higgs signal peak. The final estimates for the expected number of backgrou
nd events are similar in both cases with predictions from PYTHIA being even
slightly higher. This comparison gives confidence in the predictions of th
e PYTHIA generator for the t (t) over barb (b) over bar background.