I believe all SD cards use pins 11,12,13, being for MOSI,MISO and clock. I understand pin 10 must always be left as an output, even if it is not used by the SD. Your description of your current shield implies that pin 10 is used and thus it is used to select the SD.
The first thing you need to do check the pins on the new shield. Is it 8,11,12, 13, or is it really 8 to 13? If the latter, what are pins 9 and 10 used for? Pin 8 is very likely for select "CS". Have a look at the SD ReadWrite example in the IDE, I think it says it all. Note that CS therein is pin 4, which I believe is standard. It seems to me that all you need do is nominate the different CS pin.