Just had a listen - to my critical ear, the Schoeps have a lot more detail in the mid-highs, around 3kHz up to 8kHz. Both recordings have too much bass - levels are better on the Church, but while "true" bass is clear, top bass (around 250-300 Hz) seems a little muddy. Overall, the Churches are coloured far warmer.
Basically, to me, they sound completely different. But I'm a sound tech, it's my job to listen for these things. On the whole, the Church mics still sound 90% as good, which is a hell of a good job for the price! They just don't sound all that similar to me.