The games look superficially the same, but there are substantial differences.
1) They both use dice for activation, but they in BA they are pretty much initiative tokens, allowing one element to perform an action at a time with players alternating depending on the draw. In CoC they represent how the various elements can be activated in varying degrees of ability, they influence the Chain of Command die which is used for various player purposes. Game phases are Igo/Ugo in Coc but the turn sequence is not preset and players can retain the initiative if they are lucky.
2) Leaders in BA are mainly morale support. In CoC they also encourage elements to perform more complex actions and increases their effectiveness. An element can act without a leader, but is far more restricted.
3) Combat is more or less similar. The major difference is that BA limits the range of most weapons, while CoC assumes realistic ranges, but does take "effective range" into account.
4) BA has a number of rules to express "national characteristics" while CoC has rules for certain historical tactics and use of equipment.
5) BA is a fairly comprehensive system which offers a new player a complete introduction on the subject of WWII, while CoC assumes you have a bit of a working knowledge of WWII wargaming and have some basic understanding of small units tactics.
I'd say they are both good games, BA is a more "playful" rule. CoC aims for a more realistic approach. Both are eminently playable and fun, they just differ in some of their game design philosophy.
I will probably play both sets, though my personal preference would go to CoC because it has that little bit more crunch in it.
