Gin Slinger is right, the reason for intrucucing the alpha-numerical callsigns is to make it easier to differentiate.
And yes, almost all flights use these new callsigns. Threre are some flights that use the old callsigns since ATC at theire destinations is not able to handle the new ones. Ah, I forgot - the long haul flights will keep the old callsigns for the moment.
Another reason is, that at LH almost every transport has a LH Number. That includes the trucks used for cargo transports on the road. So with the time there were not enough numbers for flights and other transports (also including codeshare numbers for partnerairlines, etc.)
So long, DBate