I use both depending on what I am pressing.
For all of my
DTG work..I use the parchment paper (silicone) although I'm not exactly clear as to why other than that is what was recommended.
For heat transfers, vinyl and plastisol I use the Teflon sheet although it is the Teflon sheet that makes things glossier / shinier when used for a 2nd press on plastisol. Unless you have a teflon sheet with a texture.
I have used the parchment paper on 2nd presses of plastisol to try removing some of the gloss...which works to some degree but is uneven.
Hope that helps....