I found the contractions during the 3rd stage more painful, but the actual birthing of the placenta wasn't painful at all.

My first birth I had a managed 3rd stage and didn't feel a single thing. No pain, don't even remember feeling the placenta come out.

Second birth I had a natural 3rd stage and I think I sort of thought the placenta would just plop out. I started to get intense back pain that wasn't like my previous contractions. The pain didn't have a rise & fall that contractions have so I had no sense of how long it would last or that it was coming on. That made it worse because it throws you off mentally with a sort of 'senseless pain' that you have no idea when it will end. I started to really carry on and had no idea what was going on actually! My MW got me a hot water bottle and told me to push with the 'contractions' (so that's what the pain was!) and that did help somewhat. Pushing didn't hurt like pushing my baby though as there was no internal pressure of a head making it's way down. Then when I did push the placenta out it did just plop out and wasn't at all painful.

As for after birth pains- I've been pretty lucky there. I had none what-so-ever with my first baby and a few mild-ish ones in the first week with baby#2.