After reading RichFaces Vs PrimeFaces (for performance), I was tempted to use both in my web application to get the maximum benefit from both.
Do you think that is possible? What are the advantages and disadvantages?
Both are great component libraries. You can definitely combine them. But it is not true that it's 1+1=2 here. It's more 1*1=1. You should really investigate the both component libraries more closely. What exactly do you need from RichFaces which PrimeFaces doesn't offer? What exactly do you need from PrimeFaces which RichFaces doesn't offer? You need to find the right balance yourself. The one webapp isn't the other.
As to advantages/disadvantages, that's pretty subjective. Go play with them yourself. First each separately and then together. Own experience is the best experience. I myself had good experiences with PF 2.1. PF 2.2 had some serious issues in among others the datatable component. I didn't try PF 3.0 yet. I am currently working on a project which uses some RF 3.3 components and we are in a progress to upgrade it to RF 4.0. All I can say is that it's a pretty decent component library with good documentation. The full PF documentation isn't freely available anymore.