The FT doctoral rankings are interesting, but I think that they have some problems (like most of the other rankings). The stated criteria for the FT list is number of degrees granted (which doesn't make much sense to me) and placements at top 50 MBA schools (which makes a lot of sense to me, but because the numbers are relatively small may reflect more on the individual graduates than the quality of the program.) Plus, the list is not broken down by specialization, which matters a lot.
IMHO, the research rankings are probably the best that we have by way of numerical rankings, but there are still a lot of variables (your individual interest, faculty comings and goings, etc.) Here are a couple more in case you haven't seen them:
This ranking thing is a really murkey area. You will hear academics say, on one hand, that PhD programs are "above rankings" (or something similar), and then you might hear about "good schools" and "top-notch programs," which implies at least some kind of ranking. Perhaps a good doctoral program is like what Potter Stewart said about pornography
: I can't define it, "but I know it when I see it." Seriously, though, I think the situation is just too fluid and individualized for rankings; although "brand name" and "halo effect" have more impact on placements than the academic community would like to admit. Again, this is all IMHO--I'm an academic neophyte.