While troubleshooting some script problems, I noticed dd was giving very different results on an Advanced Format drive vs my old drive. Both drives should be identical, bootable copies with the only difference the sector size.

dd if=/dev/sda of=/test.dd bs=512 count=63
hexdump test.dd | nl
Replace drive, reboot, repeat.

On both drives the file test.dd reads as 32k, however a hexdump shows vastly different results. On the old drive 35 lines of hex are shown, but on the new drive 860+ lines of hex are shown. How can both files be the same size?

It worries me because I use dd a lot and want to know it is reading/writing the correct blocks and offsets. Even if I assume there should be 4x as much data on the Advanced Format drive due to a sector sie of 4096 vs 512 860 is more than 4x the size of 35. It just doesn't make sense.

So the two files (test.dd) had the same size. That is ok.
35 lines of hex data are definitely less than 32k, you should check it

That's true that 35 lines is less than 32k, but I'm not sure how hexdump deals with null characters. I think it simply omits them, so there is probably 31k of 0x00. The question is why is it different on the other drive?

yes, you can use hexdump -v to avoid omitting lines (see man page, it will skip printing identical lines)
So about your first question: dd works as it was expected, dumped 32k. The next question: why are they different. But why should (the content of the beginning of a disk) be identical at all?
Probably one of them contains a boot loader and the other one not.

Look at the drive with a hex viewer maybe to see what data is where and why.