Not sure where you're located, OP, but I just did a private transfer in CA for the first time, and the rifle is in Jail. I still have to wait 10 days for it to get out of jail.
The PP transfer was almost exactly like a DROS, other than the rifle is not shipped to my FFL, I have to pick it up at the store which the PP was done at. It was cheaper to do a PP transfer, but not by much. It cost me $49, opposed to $75 to DROS. The advantage with DROS for CA is that I can add additional rifles to the DROS for $10/ea. I did 3 rifles at my local FFL and the cost is $95. Everything is in jail, currently.
The downside to DROS is postage is required to ship it to my FFL, so it is actually cheaper to do a PP transfer.
OP, what state are you located in?