Benefits of a Buchner funnel w/ a fritted disc instead of Quantitative Filter Paper Circles
Buchner + filter paper cons:


The filtering surface is not uniform. It filters only where the holes are, so most of the surface is not working. 
Some solid can slip between the paper and the filter.  Then the filtrate must be filtered again. 
You have to cut the paper. 


Fritted glass filter pros:


Uniform filtering surface. 
Pore sizes from number 1 (coarse) to number 4 (fine). In organic chemistry, number 3 is the standard. 
Can be cleaned easily when the solubility of the product is known. 
Can be sterilized at high temperature. 


I use them almost for everything except for filtering activated carbon and very dirty unknown samples. If the solid does not dissolve in solvents, we try with concentrated caustic, concentrated sulfuric acid or strong oxidants; in that order. 

It is better to buy the ones without the vacuum connection. 
They are cheaper and have less points where they can break.