In the last couple of months my grocery store has started to sell Farm Raised Salmon and separating it from "Wild" Salmon. Any difference in cooking these two that I should be aware of?
You want to minimize the amount of fat you consume from farm-raised salmon. This means you should trim the fat from farm-raised salmon and avoid frying. Farm-raised salmon should be grilled, broiled, or baked, anything that burns away some of the fat. (Farm raised salmon is 52% fattier than wild caught salmon).
Why? Farm raised salmon have ridiculously high amounts of carcinogens known as polychlorinated biphenyls (PCBs) as compared to wild salmon, and many other foods for that matter. You can blame the feed they are given. These carcinogens are concentrated in the fat of the fish, which is why you want to minimize the fat intake. The levels of PCBs in farm-raised salmon can be 10 to 16 times higher than wild caught salmon, and up to 40 times the level found in other foods.
Experts recommend eating farm-raised salmon no more than once a month to minimize exposure.
Farmed salmon is often slightly mushier in texture than wild. It also has less depth of flavour. You will want to look for cooking methods that won't add water (grilling, roasting, frying) and have a light hand with the seasoning.
I find the wild salmon to be less fatty and easier to overcook. I take off a few degrees from final temperature to keep the texture flaky, somewhere between 125-135.
Following up roux's answer (that wild salmon has more flavour, which is true): presumably you'd buy the more expensive wild salmon to enjoy that deeper flavor. One thought is that the deeper flavor will support more additional tastes / seasoning (and it will). Another thought (which I prefer most of the time) is that the deeper flavor should be enjoyed for itself.
So, when cooking the wild salmon, use techniques that preserve the salmon as much as possible 'as it is'. Sashimi, if you're certain of the quality / hygiene, would be the ultimate expression of that.