In a less recognized article in Current Biology, Fischer et al. (2006) report on the genetic diversity of ape subspecies.
Here's the meaty part of the abstract:
Finally, we find that the extent of genetic differentiation among "subspecies" of chimpanzees and orangutans is comparable to that seen among human populations, calling the validity of the "subspecies" concept in apes into question.
Previous studies of ape population structure have mostly been based on one locus (mtDNA), with a few using the Y chromosome and nuclear microsatellites. This study adds nuclear sequences to the mix, from 16 to 26 loci. The multiple-locus perspective is important, because demographic structure can be tested only through its similar effects on different unlinked loci. The use of sequence adds a time depth that may not be as evident from microsatellites, since they have markedly faster mutation rates. For instance:
The two orangutan populations have a significantly positive Tajima's D, because of an excess of intermediate frequency alleles, which is best explained by a recent reduction in population size or by population subdivision. Using 14 microsatellites, Goossens et al.  showed that the excess of intermediate allele frequencies in an orangutan population from Borneo can be explained by a very recent decline in population size, mainly as a result of human activity. Because it would take much more time to be able to detect this effect in nuclear DNA, and because our orangutan samples come from different local groups (see Table S1), population structure is a more likely explanation of our observation (Fischer et al. 2006:1134).
Despite the conclusion and abstract, there is not too much different in this study compared to previous work. For instance, the FST estimated between orangutan subspecies is 0.28, which is at least double that estimated between human races for the same loci. Similarly, the FST between Eastern and Western chimpanzees (Pan troglodytes schweinfurthii and P. t. verus) is 0.32. These estimates show a considerably higher degree of population structure in these ape species compared to humans. The FST between orangutan subspecies doesn't represent quite the high division between these two groups, because of the extensive sequence variation within each of the subspecies.
One difference is surprisingly slight: the FST between central and eastern chimpanzees is only 0.09. This is the same as estimated between Chinese and Italians in the study, placing chimpanzee subspecies differences inside the range of human racial differences.
Or does it? The study also obtains the average pairwise difference between these populations, finding that the average difference between central and eastern chimpanzees (0.20 percent) is about the same as that between central and western (0.21) and eastern and western populations (0.20). Now, again as for the orangutans, the average pairwise difference among chimpanzee populations is inflated by the relatively great diversity within chimpanzee populations -- but not so much. FST is a measure of how many variants are shared by two populations (formally, it measures a reduction in heterozygosity attributable to population structure). So the results tend to indicate that eastern and central chimpanzees share a lot of alleles, amid a relatively high amount of diversity.
Why should that be? One explanation is a recent colonization of the eastern range (or more narrowly, the part represented by their sample of reserve chimpanzees from Kenya) by chimpanzees of central African origin. A widespread recent colonization might also explain the evidence of mtDNA disequilibrium in eastern chimpanzees.
Or, the low FST could represent a history of gene flow between central and eastern African chimpanzees. Fischer et al. apply a mixture of these explanations, which they also apply to the orangutans:
With respect to the duration of physical separation, the Dahomey gap that separates western and central chimpanzees was covered with rainforest until about five thousand years ago, and Sumatra and Borneo were physically connected until ten to twenty thousand years ago. Thus, the time of separation of the "subspecies" by geographical barriers has certainly been too short for complete lineage sorting by genetic drift and shorter than the separation of many human groups. In addition, migration between the groups may have occurred subsequent to the emergence of these geographical barriers. Indeed, we speculate that a more geographically complete sampling of chimpanzees and orangutans with noninvasive samples from the wild as well as samples from museum specimens in areas where apes are now extinct will eventually demonstrate that the overall picture of genetic variation within chimpanzees and orangutans is one of isolation by distance, as is largely the case among humans (Fischer et al. 2006:1135, citations omitted).
Naturally, both factors are important -- the initial movements of these apes to their current locations, sometime during the Pleistocene, and the subsequent movements of individuals between populations. The question of gene flow is important because it delimits the extent to which adaptive variants can spread from their point of origination -- and thereby circumscribes the degree to which all chimpanzees today may be different from their common ancestors. In other words, gene flow would allow multiregional evolution of these ape species over time.
But there's no real reason to say that these weren't subspecies. They were genetically differentiated after their initial origin and retained substantial genetic distinctions between them over time. "Subspecies" is a nebulous category, but it is generally defined as an evolutionary lineage within a species, which these populations would appear to be. They're not species, after all.
The only real question is what the spatial differentiation of these populations looks like -- are there long clines of genetic variation within chimpanzees as there are within human populations? For that, we will have to sample many more chimpanzees. For orangutans, the answer today is presumably "no", because the subspecies are on islands, and themselves are highly fragmented into small populations.
Fischer A, Pollack J, Thalmann O, Nickel B, Pääbo S. 2006. Demographic history and genetic differentiation in apes. Curr Biol 16:1133-1138. DOI link