I've used BP quite a lot for the NW Frontier. The rules system is an updating of GW's Warmaster system which I haven't played.
Basics - your army is organised into "brigades" which each consist of a brigadier and several units. You can, of course, substitute suitable titles such as Emir as suits your whim. Each unit is nominally a regiment/battalion/warband, but there is no reason why you can't scale things up or down for larger or smaller actions. Each brigadier has a staff rating, this is a number, usally between 4 and 9 that needs to be rolled under on 2D6 to make a unit act. There are a limited number of modifiers based on distance from the officer to the unit, the unit's formation and proximity to the enemy. If you roll well a unit can move more than once (this allows grand sweeping advances), if you roll poorly not only can't that unit move but your brigadier can't issue any further orders that turn. Some of this sounds a bit odd but it generally works well. When issuing orders they tend to be quite general in nature e.g. the 4th Foot are to advance to Splendid Ridge and will charge any enemy encountered. You then roll. If you have sufficient movement then you carry out the order, if not you MUST carry out as much as IS possible - this can leave units hanging out on a limb. Overall it is a fairly simple C&C system that allows for imperfect performance without massively difficult charts, tables or written orders.
Once the player has moved they may fire. Each unit has a fire rating, this is the number of D6 that are thrown to hit. A hit usually requires 4+, but there are modifiers. 6s disorder the enemy, which basicaly means they can't receive an order in their next turn (in effect they miss a move -but can still fore at a penalty). Any hits are then subject to a saving throw by the target (this is termed a "morale save") - usually again this is a 4+ but can be modified. Each unit also has a "stamina" rating, this is the number of hits that can be taken. If the stamina rating is matched then the unit becomes "shaken" and suffers penalties, can't initiate charges etc. If the stamina is exceeded then the unit must take a "break test" which can result in "hold ground", "retire" or "break". There is no casualty removal, units acquire hit markers instead (wounded/dead figures are recommended, but we use nice little wooden markers) - therefore within reason basing is irrelevant as long as all parties agree. There is also no recovery from a "break" result, the unit is dead. Note that this is the ONLY way a unit can die. It seems odd on first reading, but you do get all of the same effects as with more traditional rule sets.
Hand-to-hand combat is generally similar, but units have a separate rating for h-t-h combat.
The core rules are generally very simple - I've written the above without referring to the book, and in most cases we rarely refer to the book during play. In order to insert flavour to individual armies there are also a series of "special rules" to apply to units- these are again quite simple and allow things such as re-rolling misses in h-t-h combat for units that are particularly good at h-t-h, bonuses for lancers charging, bonuses or re-rolls for morale. These are all quite simple and are presented separately ratther than being mixed into the main text as caveats.
The core rule book includes sample scenarios for both the Sudan and AZW with stats for the combatants. I believe that there are suppliments in prep for both conflicts. As written the units use a lot of figures and a big table, but most people halve move distances and at least halve the unit sizes - but again as there is no casualty removal the number of figures doesn't actually matter. We often use as few as 4 - 8 28mm figures for smaller units and get an excellent game.
To give you an idea of what a standard unit looks like a British line regiment has 3 dice for shooting, 6 for hand to hand combat, a morale save of 4+ and a stamina of 3. This is pretty much a "default" profile. However, added to that they are usually "Steady", which means they automatically get a 12 for their first break test which is usually enough to pass.
A unit of Beja spearmen (and I have had to look this one up!) has 6 for h-t-h, 1 for shooting, 4+ morale save and 3 stamina, however they are fanantics which basically means they MUST attempt to charge whenever possible.
As a final note, I'd say that the rules are designed very much as a "game" and are for "fun". There are loopholes in the rules, but it is very much intended to be a "shared entertainment" between gentlemen. Dullards and lawyers are not welcomed. I like these rules, they aren't perfect, but they perfectly suit where I want to be with my wargaming these days.