Here's some testing I did of Billmen...

Billmen (armour upgrade 1) vs Armoured Sergeants (HUGE unit settings, med difficulty, grassy plains. Billmen always listed first, deployed in three ranks to get similar unit width as spears have in four. Numbers listed are remaining men at the time of rout).

73 - 67 (Billmen win, Sergeants lost approx 50 on billmen charge)
71 - 62 (Billmen win, Sergeants lost approx 50 on billmen charge)
48 - 79 (Billmen lose, Sergeants lost appox 30 on billmen charge)
84 - 70 (Billmen win, Sergeants lost approx 55 and general on charge)
67 - 54 (Billmen win, Sergeants lost approx 45 on billmen charge)

The numbers aren't scientifically gathered, they were grabbed by me without pausing just because I wanted it done quick, but they won't be more than 3-5 off at most, which gives a reasonable variance for accuracy. They stand up quite well against good spears. :)