Two things come to mind. First, the "China" card may not be designed to work in SPI mode since 99.9% of the people buy SD cards to work with things other than Arduinos
Yes, the SD spec says all cards must work in SPI mode...but if you can sell cards to 99.9% of your customers without complaint, they get away with it.
Second, it could be hardware differences in the card causing communication problems. Many people have noted that using resistor level shifters with SD cards often causes problems. That's not to say this is the problem in your case: the Stalker is a 3.3V board so there is no level translation. It does, however, highlight that SD cards are sensitive (in general) to the quality of the digital signal. I don't know how the Stalker is routed on the PCB but if the traces are "long" there could be significant ringing or reflections on the SPI lines. The Kingston card tolerates these, the China card may not.
The Flexible MIDI Shield
: MIDI IN/OUT, stacking headers, your choice of I/O pins