Johnbear44: As the author, I can give you an idea of how it plays, though since I haven't played BA or BA 2, I can't necessarily compare the two.
I have played CoC and can say it has a more natural flow for combat and picks up some elements of platoon level combat few other systems do.
First off, it does allow you to break squads down into parts, but the way the rules work, you can easily move and fire with more than one team, allowing you to perform squad tactics easily and naturally. It uses Tactical Points to perform actions, so when a unit Activates, it gets three Tactical Points that allows you to move or shoot in any combination. These points can be shared by nearby units. SO you could use a Tactical Point to rush a rifle team across a street while the LMG covers them. Or, with sharing movement Tactical Points, the whole squad could move together. This makes movement and shooting very naturally flowing on the fly.
Some of the unique mechanics are the scenario deployments which use a double blind system without the need for record keeping or maps. This means the attacker and defender set up five each locations on their side of the table as places where the defender might place units and places where the attacker will deploy from. Units are kept off table until, for the defender they are revealed by fire or coming into close contact, or as the attacker they are brought on the table to advance. This means the attacker is truly advancing into an empty table and he must use good tactics, cover, and a sound plan to attack successfully. This "empty" battlefield really creates tension without the need for maps or record keeping.
This also plays into the next unique element. The core game is based around a battlefield representing the 50m of space in a platoon attack, so unlike many platoon level games where both players grab full platoons and slug it out with support weapons and tanks, this system creates a much more realistic situation for each player.
The defender is only allowed to use one squad to defend his side of the table. Platoons typically defend a 100m or more, and so on a table as small as 50m, only one squad will be on the line. The other will be in reserve and the other somewhere else off the table. For the attacker, he will be using his full platoon of two squads on the table attacking with a third in reserve. This means the defender will have to place his units and fields of fire carefully.
Another unique rule is "first fire". This is where the first unit to open fire (usually the defender) has a major firepower advantage. Much like in the AARs of real combat, an attacker advancing into the unknown is often surprised by the first hidden MG to light him up. This adds even more tension to the game.
Lastly, one of the unique elements of the game is how players may use support weapons off table. HMGs, AT guns, mortars, etc. can all be played as off table support with mechanics to provide HMGs with beaten zones and cones of fire (HMGs can now be true area denial weapons instead of just more dice). Mortars can be dialed in and create areas where the enemy will not want to go. Creating beaten zones and dialing in mortars is as easy as placing a marker. Beaten zones can be traversed as well, and mortars can adjust their fire also on the fly all using the already mentioned Tactical Points. Again, this allows for a very easy and natural flow using a set of very simple mechanics, but allowing players to do a lot with them.
I guess Teppsta can recommend CoC. It is a fine game (though IMHO overrated). But I'd say give DH II a try. I think there is a LOT there you will enjoy and I think you'll find it suits your request.
Check out the Bootcamp links listed by Brigade. I think they will give you a good idea of how a turn plays.
Thanks!
Keith