I have installed miles of both. There's a lot of things to consider, and initial cost is down the list from my POV.
What kind of dog? Are you just putting the fence in to confine the dog or do you hate your neighbours?
How high? Some dogs can easily climb C/L.
Maintenance isn't that big of a deal. Wood fence, properly stained when it is installed will last for years before it needs to be redone. Some wood fences I put up in the early 80's are still working fine.
Aesthetics? Some wooden fences can be very attractive and an integral part of the landscaping. C/L not so much.
C/L offers different colored vinyl or privacy slats, but it's like putting lipstick on a pig. Makes for a sexy pig, but still a pig.
I like a kennel with a concrete slab for a dog, and a fence for part of the landscaping.
I did put in nearly 400 feet of grapestake fence spaced a little narrower than my Jack RusselX. Stained both side white. and then redid the railing and panels around my second story deck to keep the little turd in. Of course the deck panels were custom made with no gap bigger than that dog.
A couple weeks later she got past one of the kids and ran out in front of Mr Singh's van. That dog is nearly 15 years old now and slowing down.