I would suggest Rhodamine 6g to study it's adsorption on AuNPs and AgNPs.
With respect to the sub-question : Analytes containing nitrogen groups, thiols and phosphines will effectively adsorb onto AuNPs. These groups can also bind to AgNPs, but analytes containing carboxylate groups and amines should bind more effectively on AgNPs as compared to AuNPs.
Quoting from rom the paper “The effect of the irradiation time on the enhancements obtained in the SERS experiments using the metallic NPs prepared was evaluated using 4-ABT for Ag NPs. Similarly, 1,2-bis(4-pyridyl)ethylene (BPE) was used to evaluate the optimum conditions for the synthesis of Au NPs. These analytes were selected based on the affinity of the compounds with the corresponding NPs”.
Although,in my limited knowledge, I don’t know any molecule that adsorbs onto Gold and doesn’t adsorb at all on silver.