We had this discussion recently with our pediatrician at our daughter's 2 year well-baby visit. He asked how we were disciplining her.
We commented that she has a different personality than her 3.5 year old brother, and while we try to be consistent and fair, we parent more to the personality.
I work with someone who is an only child and has an only child (9 year-old son). You'd never know. She's very disciplinarian with him, and has incredibly good parenting despite him being the sole source of her attention.
All children have different personalities, and that really needs to be taken into consideration. But, we're going to have the same punishments for the same bad behaviors as well as rewarding the good ones.
As the 3rd of three children, the worst thing you can do is to rear them totally differently - different rules, different punishments, different praise. Be fair, be true to the child, but be consistent.
I remember my sister getting straight A's for the first time in either 7th or 8th grade. My parents threw a freaking party for her. I also had straight A's and barely got a pat on the back - it was expected for me because of my past academic performance (I am 2 years younger). It stung to see them making such a big deal for her when I'd had the same accomplishment at the same time.
She was also never grounded - I was a great kid, but I was grounded all the time. There was, and still isn't, any fairness.
At the end of the day, the most important thing we can do for our child/children is to let them know how much they are loved - even if it's tough love - and how proud we are of the person they are and will become.