If you start out with a larger sample you can go down to smaller subsamples without having your MOE explode.

Example with AA

PPP: 2300*.18 (N=414) (AA) ~MOE=5
SU:  700*14 (N=93)(AA) ~MOE=10

So, PPP has a MOE of 5 for their AA numbers of Obama v. Clinton and SU has a MOE OF 10.

For a 99% confidence level, MOE is about 1.26/sqrt(N), where n is the number of respondents.

In either case, however, the larger sample size for PPP means that it is more precise (as in repeated polls will give about the same result), but not necessarily more accurate. One obvious case would be the infamous Literary Digest poll that had tens of thousands of respondents and showed Landon easily beating Roosevelt. Obviously, either SUSA or PPP has made a significant methodology error, and we can't tell which one it is at this point.