I am not a specialist in measurements of heavy metal pollution, but if you go to the bird literature dealing with pollution in Google scholar, and look at the methods sections of these publications, you will probably find different methods (e.g. T. Eeva in Finland or M. Eens in Belgium for publications, or people from Annaba, Algeria, etc....) .
I am sorry, I used AAS only in one research, and since that time I did not need to determine either havy or other metals. As for the other methods, as stated by the above answer authors, maybe ICP-MS provides more precise data.
I have not use ICP-MS before but you can try it as pointed out, I only know of AAS of which the precision depends on the integrity of the calibration of the AAS machine used.
ICP-MS or ICP-OES can measure several metals in one run, use less sample volume and are usually much more accurate than AAS (lower method detection limit), but also more expensive to run. This link has a lot of details on ICP: http://www.inorganicventures.com/icp-operations-guide
Also check this review paper: Bolann et al. (2007): Evaluation of methods for trace-element determination with emphasis on their usability in the clinical routine laboratory
Some of the newer model ICP-MS can even measure Hg down to 0.01 ppm.
ICPMS can be used to determine very low concentrations of heavy metals (down to ppt level) provided that the acidity of your digested sample is not too high. We have succesfully measured most of the common interest heavy metals in biological samples. BUT... keep in mind that ICP is far more "expensive" analysis, and if your concentration level can be determined by AAS, it is a waste of resourses to use ICPMS. Additionally, ICPMS is strongly effected by the sample's matrix, which means that you actually need to set up the method (probably starting from the digestion) specifically for the kind of sample you want to analyse.
ICP-MS is one of the best methods. Instrumental neutron activation analysis (INAA) is also an excellent methods but requires a source of neutrons. NAA can perform non-destructive analyses on solids, liquids, suspensions, slurries, and gases with no or minimal preparation.
Both ICP_OES and ICP_MS are very good tools for measuring metals. They both have some advantages over AAS. These are the methods currently being used for measuring heavy metals in the US-EPA methods. Both these techniques require sample preparation similar to AAS methods. One of the advantages of these methods is that they are faster than AAS when looking for multiple metals since no hollow cathode lamps are needed. They can be more sensitive for many elements and they have broader linear dynamic ranges. The disadvantage of these two techniques is that the instrumentation is more expensive to purchase, and their operating cost are higher. In addition they are somewhat more difficult to operate and maintain than AAS. It is generally considered that if you are only running a few samples (less than 10) and looking for a only a few elements ( 5 or less) AAS is the better choice based on cost considerations. The literature is full of papers using ICP for metals analysis in a wide range of matrices. You need to evaluate your specific needs and compare the three techniques to determine which is best for your laboratory.
Use of ICP-OES and ICP-MS is widely used nowadays. We are routinely using them for determining heavy metals like Cd, As, Pb, and Hg from powdered plant samples.