BFBC is basically just a Battlefield spinoff.
MOH and BF are two distinct franchises; in PC terms the former was/is standard FPS fare, whereas BF is focussed more on large scale multiplayer.
Also worth noting that the BF series predates EA's ownership of DICE so it's not as though they had two studios launching 'the same' franchises under their banner.
Finally a lot of people forget these days that EA are first and foremost a publisher (and one of the biggest at that), so it isn't that surprising that they should be publishing games from different dev studios that have similar content, it has always been that way.