How to use the data CRC of SD cards in SPI mode?
So, regarding the two "CRC-delivering cards": It's kind of hard to debug this without any example data and CRC, but the most common problem one encounters is that the generator polynomials are "meant" the other way around, ie. whether \$x^0\$ corresponds to the first or the last bit. 

Checking is easy: just have test data that you have both in original and reversed bit order, and see what makes sense.

Now, you've tested with 0xFFFF and 0x0000 already, which are symmetrical. At least for 0x0000, the result of a polynomial should definitely be zero, shouldn't it? What are you expecting, what are you getting?

Reference:

http://users.ece.utexas.edu/~valvano/EE345M/SD_Physical_Layer_Spec.pdf , p. 54f