Star Trek's Borg famous claim "resistance is futile," and I think the same is probably true for wargame designer Richard Borg's creations. I know I haven't been able to resist buying anything related to his Commands & Colors system. I'm not alone in the collective, either, as Borg's designs are among the most popular wargames ever published.
Still, sometimes you have to choose and prospective purchasers may wonder which is the best choice for them. Each game has its vehement fans, but here is what I believe is a fairly objective rundown of their strengths and weaknesses.
Really, they are close enough in quality and game play (with the possible exception of Battle Cry) that I think the main consideration should be which theme a player finds the most interesting. pick that first.
From purely a game play perspective they each have strengths and weaknesses.
Battle Cry (American Civil War) is the weakest of the lot, simply because it was the first, and the subsequent designs have all refined the concept. If Battle Cry had expansions like the others I'm sure it would have kept up, but it's a one-off design.
Command & Colors: Ancients (Ancient battles of the Classical Era) matches its era well and is probably the most tactically intricate because of all the different troop types, which often have fairly subtle differences between them. Terrain plays a smaller role in this game than the others as ancient armies tended to fight on the flattest and clearest terrain available.
BattleLore (fantasy but also historical medieval) is similar to C&C:A, especially when played with the Medieval Rules. Adding Lore adds some interesting new twists to the game system. The fantasy aspects of the game are not overpowering and it is still an army-level game and not a sort of role-playing experience.
Memoir '44 (World War II) is a lot more about terrain and combined arms effects. The interaction between the units is more subtle than it is in C&C:A because of the long ranges involved. Just because units are not near each other doesn't mean they don't affect each other. And the air pack adds a new dimension of course. There's more variety in the scenarios compared to the other games, which are almost all line-them-up-and-fight battles, with a few notable exceptions.
You may also want to consider how they are marketed.
Battle Cry (Hasbro/Avalon Hill) is a single, self-contained game, but it's out of print.
BattleLore (originally Days of Wonder, now Fantasy Flight Games) and Memoir '44 (Days of Wonder) each start with a self-contained base game that you can add to as finances and interests allow, although that may change for BattleLore as it is moving to a new publisher. While some of the expansions require parts from other expansions there are always scenarios that require nothing more than the base game and that particular expansion to play.
C&A:A (GMT Games) has a self-contained starter and then each of the expansions is a major purchase as well. These expansion tend to build on each other, so I would say this series is something you'd want to commit to in a serious way to get the most out of it.