From what I understand, Rev B used a single-core Zynq device, and I've noticed the part number listed on Rev C is different. Does the new revision contain the usual dual-core Zynq 7010?
No, the Zynq is the same on both - XC7Z010-1CLG225C4334 have a look at : wiki.analog.com/.../hardware
Yes the FPGAs are the same.
It appears as though the new revision does not show the 4334 line in the comparison images. Does your answer mean that it is still a single core device?