I think it's a bit of both.
My parents rescued a Border Collie and some cats from an empty flat just before I was born and they found homes for the cats and kept the dog and when I was born, Dad said that she would sit by me constantly and she accidentally nudged my pram, making it rock as I was crying one day and it soothed me and from then on, if ever I started whimpering in my pram, she'd sit in the basket and use her nose to bounce my pram. She would also escape by jumping over our gate and would follow my Dad if he took me out in my pram - he left me outside a shop one day and came out to a commotion of a dog barking and Lady had followed Dad and made herself comfy under my pram and she was upset because two ladies were leaning into my pram to look at me (the ladies actually admitted to my Dad that they'd come too close and that Lady was just protecting me).
Another time, Dad had taken me to my Nanna's and not long after we'd arrived, there was a knock at Nanna's door and when she opened it, Lady was there, wagging her tail on the path.
Sadly I don't really remember her but I rescued a Border Collie 15 years ago (her breed was pure chance but when Dad saw her, he said she was just like Lady) and she was amazing and always eager to please. I was really ill one day and bed bound and I dropped my medication packet and she was playing in the room and lunged for the packet and I thought "Oh no!" and she came and gently placed them in my lap and then carried on with her playing.
I miss her terribly.
Now my husband and I dedicate ourselves to giving rescue Border Collies a loving forever home.
Currently got a male and a female (both neutered) and they both trained well but I think that was more to do with them than us.
Our lad taught himself how to flip a doughnut shaped toy into the air and then catch it every time but he is definitely the more bonkers one. Our new girl has the strongest herding mentality (she likes to herd bubbles - our other female liked to herd balloons whereas our boy thinks it's his mission to destroy all balloons).
She taught herself to go and find the cat (who likes to hide) - I ask where he is and she will go all over the house and garden to find him and will then sit next to him and bark for me.
The cleverest thing they've done was this summer - they have a shallow paddling pool to play in on the hotter days and I'd just popped in to put the kettle on and my girl came running in to get me (I can't explain it, maybe it's because I've been a "Collie Mum" for 15 years, but I just knew she wanted me to go outside, rather than an ear tickle) and I followed her outside and our boy was looking from me, into the pool, to me again and she ran to the pool and our boy actually took the running hose out of the pool with his mouth and I saw that they were looking at a drowning honeybee - thanks to them, I saved the honeybee but I still can't get over our lad pulling the hose out!
From my personal experience, I'd say the female Border Collies are easier to train and are more "sensible" but they're also very bossy when they want to be - when my girl fancies "herding bubbles", she picks her bubble tube up and brings it to me and if I don't respond quick enough she starts tapping me on the knee with her paw.
Mind you, she can be a moody little madam too - a few weeks ago she couldn't walk between the sofa and the coffee table because my leg was in the way and she really bad temperedly yanked my leg out of the way by pulling it with her paw.
They are intelligent and very beautiful (but I think the same of all dogs, even my ex neighbour's untrained one) but I do admittedly have a huge affection for Collies, even collies that are different types and mongrels that have Collie in them - they all just seem to have this way of learning really quickly and wanting to make those they care about, happy