RDP uses the Bergeys taxonomy, which is more conservative and standard. Silva and Greengenes use their own taxonomies which are developed by their own teams and collaborators. For some groups, collaborations have improved the taxonomy and may help you if you are working with a specific groups of organisms. E.g. Silva has a nice eukaryotic taxonomy.
Another key difference is that with RDP the lowest taxonomy level is genus whereas you can go to species and strain. Having said that, I will not have a lot of confidence working at strain level if I have a 100 bp read.
If you are working with the human microbiome, the thee of them will do a good work since the human-related microorganism are better studied that some rare phyla.
Just to add to satanicodr's answer, one of the main differences between Greengenes and Silva is the way in which the tree is built. Greengenes construct a de novo tree; Silva use a seed tree and add extra sequences into it parsimoniously. There is a tradeoff between these two methods in that a de novo tree should give the most accurate topology of the sequence data however it is more sensitive to poor quality sequences or chimeras.
Differences in taxonomy arise due to differences in the topology of the tree causing sequences to be grouped differently into monophyletic groups. This is also compounded by regions of the tree that are only known by environmental sequences where the names are up to whoever is curating the tree and naming these groups. I known that the people behind both Greengenes and Silva are working on trying to standardise the naming in these instances.
Greengenes or Sliva will serve you well but I use greengenes because I prefer the de novo tree construction (and because one of my PhD advisors is the curator).