They are based on the Black powder rules, which I'm familiar with.
There are some diffrences, while I have a good understanding of combat and tactics of the 18 and 19th centuries, I'm a total noob when it comes to ancients.
Therefor, while I can say something about realism of BP I can't really say the same of Hail Caesar.
The first thing I should say that it apears that the book has less eye candy, I havn't taken an exact count of the number of pictures of figures, but there apear to be less of them in this book.
Here are some obvious diffrences, while in BP you can shoot the enemy to pieces, but in hail caesar, you are before the use of the long bow, and musket, while the rules do strech into the period of the long bow, you would need some special rules for them, because in this ruleset, ranged fire is probebly never going to break a unit, infact fireing long range at heavy infantry is at best going to be anoying for them, but thats it, stones and arrows, won't go through a heavy laminated shield then armor. A volley of .79 on the other hand would. Yes, if you get 20+ arrows in your shield it might be hard to use.
So really the only way to break enemy is to go all out, no kissing or boob tuching, but full on 3rd base. In BP most units have 3 in stamina, that means they can take 3 hits, while in HC it's 6, meaning combat lasts longer.
Also almost all infantry has a short range ranged ability, this is a a mix of infantry with javelins or just a few warriors darting ahead of from troops taking a stabb at the enemy.
Anoher diffrence is more formations. In BP you had line, column, square, as well as mixed and skirmish order. In HC you have 2 deep line, 3 deep line, 4 deep line, 4 deep phalanx line, warband, skirmish order. In BP you mostly have line infantry, light, medium and heavy cav. Other then that you got light and guard infantry. And some generic artillery that are mostly the same.
HC got light, medium and heavy infantry, archers/slingers, you got catapracs, heavy cav, medium cav, light cav, horse archers, you got diffrent types of artillery, oh and ELEPHANTS!
The command and control system is more or less the same as BP, units can get up to 3 moves, the movies are shorter then PB only about 6" for infantry, so up to 18 inches of movment for infantry, conpeard to the 36 in PB, that means, you don't need the MAGA FUCKING HUGE table like you do in BP, granted there is no problem changing this in BP.
There are small other diffrences in the command and control system to make it less about fast sudden changes, into a more controled steady move into contact.
What this does, from reading the designer notes and just from reading the rules, is that it's less about exploiting a sudden opertunity, then making a good battle plan, a good deployment and sticking to it.
There is somethings I find a little od, the game uses "divisions" this is to help control the battlefield, and the unit is well not that defined.
While in BP you have simply a battalion or cav regiment as a unit, this is not as clear cut in HC.
While unit, works great for lets say Roman imperial cohort, it dosn't work that great so for everything, like Republican romans ect.
What exactly should a division be? It will be very diffrent for each army I think, I the end I went for each legion should be each own division. So my army might have 2-3 roman legions(divisions) 1-2 allied divisons and 1-2 cav divisions.
The game is more figure heavy then what I think most ancient rules are, I think some of the DBA or DBM or IBM or BMW what ever have single units with less then 10 figues.
And while you CAN play HC with those units, I think most will play with much higher figure rations, I'm doing 20 figure units for 2 rank infantry, with 4 rank, that is 40 figures.
I still havn't decided on size of cav units, I'm gonna have a look at historic cav formations and see what works best.
So my finnal thoughts of the rules, I think they have lots of promise, I would have liked more info and battles with republican romans. It will be fun to see if can stick with this project, or if it's going to be still born.