There is no objective way to measure anatomical similarity, but you can get a sense by converting character matrices into distance matrices. I've done this for the matrix used by Diogo & Wood (2011), which looked at soft tissue anatomy. Here is a bar chart showing how similar each taxon is to humans:
|Dangit, 2011, not 2010. I'll fix it later.|
Click for full size.
As you can see, the distances for great apes are well-marked and exactly what you'd expect based on phylogeny, but past that it gets a bit fuzzy. Moving outward from the great apes we get to Old World monkeys, then gibbons (from phylogeny you'd expect gibbons first, but the difference is so minor I'm sure it's meaningless), then a mixture of non-catarrhine primates, and finally non-primates.
Expect to see some more stuff like this on A Three-Pound Monkey Brain soon.
- Diogo & Wood (2011). Soft-tissue anatomy of the primates: phylogenetic analyses based on the muscles of the head, neck, pectoral region and upper limb, with notes on the evolution of these muscles. J. Anat. 219:273–359. doi:10.1111/j.1469-7580.2011.01403.x