Two Lurchers here.
Pros:
Incredibly placid, quiet and lazy in the house.
Very gentle and playful with the dcs.
Extremely loyal and loving. Love cuddles and planting their backsides - in order of preference 1) on your lap 2) on the sofa (where they know they're not allowed).
Absolutely beautiful to watch when running at full speed. (As long as you make sure you keep an eye on them, as you really know about it if they bump into you going full pelt!)
Incredibly calm and patient, even at the vets where I have been able to hold both of them at the same time while one had needle biopsies taken.
Ddog1 is highly sociable with all other dogs and also very gentle and sensible headed around them. (Not so ddog2 who is afraid of off-lead dogs, but that's due to bad life experiences and not breed specific.)
Both have excellent recall - although in all honesty this isn't a breed trait, but the result of lots and lots and lots of training, both when they were young and ongoing.
Cons are different for each dog, probably due to them actually being crossbreeds and having very different starts in life:
ddog1:
Is a total glutton that lives for food and will indulge in binnie-pigging (as it's known in our house) at any/every available opportunity, as well as stealing treats/food off ddog2..
Has a beautiful grey brindle coat, but sheds worse than any of the other dogs we've had over the last 25 years, including GSDs.
Has a tendency towards separation anxiety, although technically it's isolation distress, because he's fine as long as he has at least one other animal with him and he doesn't mind who/what that is.
Is an obsessive time-keeper. Knows what is going to happen when and is the most dreadful nag if he thinks his routine has been broken. That's when he employs his rather spectacular Wookie voice to make sure we completely understand how much trouble we're in. 
ddog2:
Has seemingly intractable separation anxiety and being with ddog1 or anyone other than me is zero consolation for him. (We have tried absolutely everything and he has improved, but we're aware that he's never going to be able to be left for longer than an hour max.)
Is generally needy and anxious in character.
Seems to have extremely faulty brakes (not good for a dog that can run as fast as he can) and as a result is regularly sporting an injury of one kind or another, including several trips to the emergency vet to get him stitched back together. (This is fairly typical of the breed as the combination of moving very fast and having very thin skin is not a good one.)
Is a bugger for nipping when playing chase (this is common with Lurchers) and regularly pulls chunks of ddog1's fur out of his bum as he races past, so now has to be muzzled when off-lead, despite not being aggressive.
Has turned our back garden into a muddy race-track with his laps of honour, flinging toys all over the place as he goes.
As I said, Lurchers are crossbreeds and that does make a big difference. Ddog one has what I know know is actually Bearded not Border Collie in him and is a lot more thick-set and square on his legs than ddog2. He also has Deerhound in him and is ridiculously good natured, patient and gentle and less 'working type', not being all that interested in 'hunting' type behaviours. He's 10 next month and in his whole life I have only really seem him perk up twice - once when we walked into a field to find it literally covered in rabbits and once three years ago when a deer shot out of a hedge right in front of us. He was on lead both times, so didn't give chase, but was definitely excited.
Ddog2 has much more Grehound in his mix, with probably some Saluki as well and is generally more anxious and needy, but also much more comical and a bit of a fool - he makes me laugh every single day. He is also far more natural and game and hasn't as yet, but I feel has the potential to take off after prey animals far more than ddog1 (hence all the hard work on recall/whistle training.)
They are very different characters, which I think is partly down to their mix and partly to their very different starts in life, but the core stuff of being calm, quiet, loving, gentle and lazy are typical for Lurchers and they are both fantastic family members that fit very well in a house with 3dcs.