I am getting chicks this week,
How old? Where from?
and I am looking for the pros and cons of keeping the brooder (protected by fencing) in the same coop.
If they are from one of the hatcheries we typically use. there is very low chance of them bringing in disease or parasites. If they are from a feed store the risk goes up a little but I still consider the risk pretty small. If you are hatching the eggs yourself the risk of them bringing in anything is pretty small. If they are from a private individual, the risk goes up a lot. The older they are the more opportunity they have had to become infected or infested.
It is possible your flock has a disease or parasite they could give to the new chicks. Some flocks have flock immunities where they may be carriers but have an immunity to the effects so you would never know they had anything until the new chicks were affected. It's not just your existing flock at risk, it is also the newcomers.
Instead of raising the chicks in a sterile environment and then tossing them into the environment they will be living in, I try to strengthen the chicks' immune system by exposing them to that environment at a very young age. If a chick is raised by a broody hen they get that exposure naturally. If they are in a brooder I feed them dirt from the run where the adults are to get grit into their system, get them any probiotics the adults have, and start them on any flock immunities they might need. They are going to be exposed at some point, I prefer that to be in the brooder where it is easier for me to observe them. I also think it important to keep the brooder very dry.
To me, the pros include strengthening their immune system.
If they are raised with the flock where the flock can observe them integration is usually much easier.
They are typically exposed to temperature swings. I believe the best brooders have a spot warm enough in the coldest of temperatures and a spot cool enough in the warmest of temperatures. They feather out faster and get acclimated if they are exposed to those temperature swings.
To me the biggest challenge to brooding them outside can be those temperature swings. I've had it go from below freezing to the 70's Fahrenheit (-3 C to 21 C) in less than a day. The brooder needs to be able to handle whatever your swings are. That's easier to do if you are in a climate controlled area.
If you brood them in your house they create a lot of dust, can be loud, and can stink, especially if the brooder gets wet. That dust can consist of chicken dander (bits of down, feathers, and skin), bedding that they scratch into tiny bits, and dried poop that they scratch into dust. Even if you don't have an allergy to chicken dander do you want to be breathing that stuff? Some people really like having them in the house while others find it to be inconvenient.
A con to raising them in the coop is that they can be easier to tame if they are convenient to you to handle. Going out to the coop to tame them is more inconvenient if you want a lap chicken.
How you feed and water them and clean the brooder may make either location a pro or a con.
That's all I can come up with off the top of my head. Good luck!