I had one with dd1 at 16 weeks and this one at 17 weeks and loved them both.
They're so much more personal and relaxing than the nhs ones, I know they're for anomalies etc and meant to be medical but I found I got very anxious for those ones as they are specifically looking for things wrong plus the sonographers were busy taking measurements and typing things in other than discussing the baby (which I agree is how it should be).
The private ones last around 20 minutes and they spend time showing you all the individual bits and chatting about them, you also get to see them in 4d which is nice but be aware that at 16 weeks they aren't very padded out so you wont see a cute chubby baby 
Regarding telling you the sex our sonographer said they check 3x thoroughly and have to be sure that if it were their baby they would be confident to buy pink/blue before announcing it, if they have any doubts they will either ask you to go for a walk and go back or return the following week.
I've felt differently about both of my daughters once I knew what sex they were too, more bonded in a way, they suddenly became 'she' and not 'it' plus I love being organised and it's been lovely preparing for them, I've never been interested in the whole 'husband announcing it' at the birth and after my first which ended in a room full of people being there because she was in distress I know the whole moment would never have been special anyway because we were both so focused on her being ok than what sex she was.