A nest survey would yield the most accurate estimates of breeding population size in a confined area. See www.globalraptors.org for more papers on this topic, and free pdfs of most of them can be obtained from [email protected].
It all depends on the exact objective. If you are only interested in the breeding population a nest site count should yield the most accurate estimate. However, since vultures often start breeding late in their lives this count will underestimate the total population sizes as it does not account for immatures. Also the larger species may not breed every year, so you will also miss sabbatical birds.
A road count may give you a more complete estimate, but you may be counting not just local birds but also birds from outside your area that visit the area while searching for food. It depends if those birds are relevant for you objectives or not.
Vultures will inevitably move in and out of any area, regardless of its size. Even breeding birds will range widely during the non-breeding season (and sometimes during the breeding season).
Road transects really only give an index of abundance, which is very useful to assess change over time. A nest survey will give an indication of the actual population - and this can also be used to assess change over time. However, exhaustive nest surveys are usually more expensive and time consuming (depending on the size of the area), so for this reason road transects are used more often.
First prize is complete nest surveys combined with extensive road transect data. The first is obvious, but data from the road transects (if they include age and, where possible, sex) will enable the total population to be estimated better (because the proportion of non-breeding adults, immatures and juveniles in the local population is better known).
count of living nests and concentrations of birds on carcasses (we used artificial feeding too) can give you objective picture of dencity of Vultures and number of nesting pairs.
I may be late to this question, but Yula Kapetanakos a scientist at Cornell University uses a different approach to census vulture populations. You can check further information here: https://www.allaboutbirds.org/news/decoding-feathers-for-cambodian-vulture-conservation/