DD had two squint correction operations on the NHS for an extremely bad squint that was way beyond cosmetic. We were very pleased with the results but with a couple of caveats that you should probably know about.
One is what Ineverpromised said - it is much harder to establish binocular vision, although DD has some now, which is great.
However, this required some work from us, which is my caveat two. All the NHS does is operate. They did this very well, but we then organised the vision exercises which have helped the 3D vision (they said it would not help, it did; fwiw I also think it has prevented the squint recurring).
Caveat three: they were very clear with us that things can change again as a child grows and so DD may need another operation as a teenager to tighten things up.
DD's squint was so severe (think one eye permanently inturned by her nose) that we had no choice, I don't think. But in the case of a less severe squint, I would definitely go down the glasses and exercises route first.
Pretty much everyone though, will do patching first, to make sure that both eyes are working equally - without this there is a risk of functional blindness in one eye, so that's the priority, quite rightly.