My dd is 17 and it's just been the 2 of us for 15 years. I'm facing the empty best in next few years and honestly dreading it!
To answer your query - I actually found 6/7/8 to be the worst years.
As they get older you get to see them really develop their personality ESPECIALLY their sense of humour, but that said dd and I have an 'in joke' from when she was 3 that is still guaranteed to crack her up with a hint of a reference from me - some things from their earlier years stay along with you both.
But... Yes we've developed more in jokes, habits peculiar to us, favourite mad meals, films, books, tv shows & music (get to fool yourself you're 'cool' again cos you know what's no 1 - at least until you get the perfect eye roll) , what I really love are our debates! I'm very politically engaged and have raised dd to be the same, that the news & current affairs are important, as is history and to not blithely accept doctrine or authority - yep walked into that one! 
So while initially she seemingly held the same opinions as me as she's grown and had her own experiences she's developed new ones, disagreed with me and even on occasion persuaded me to change mine.
But yes, conversation generally becomes much more interesting.
There's SO much more you can do with them when they get older, because they develop longer attention spans, better physical ability & confidence, more patience, more willing to try things that they previously saw as 'grown up and boring'.
They can help more and you need to do less of the annoying stuff for them - child labour - bring it on 
You can find a camaraderie in cooking together but also in how hard it is to change the bloody bed!
Tips & tricks that would not impress other adults inspire awe in your learning it for the first time teen. (In other words you get to show off a bit)
Not having to play snap for the 100th time! Or I spy where they've had you guessing for 2 hours getting it 'wrong' because they said the wrong initial! Being able instead to play really good games with them including introducing them to your favourites - dd LOVES game of life and scrabble.
Trust us - the best is yet to come!