Do fresh local eggs have more omega-3 than supermarket eggs?

No. All eggs have the same unless they are fortified.

There are plenty of other dietary sources for omega-3s.

I say go for the delicious, unmatched taste of fresh eggs if you have them available.

The farm I work at has about a thousand egg laying hens. Their eggs are the same as store bought in terms of nutrtion but are MUCH tastier.

So, what does your generous neighbor get in return? ;^)

It all depends on what you feed the chickens.

That said, backyard chickens often get to eat weeds, bugs, and other goodies they scratch up. Supermarket eggs are from chickens that are fed just enough to keep them alive because any more cuts into the profit. There are exceptions (like chickens fed a high omega-3 diet). As a whole, the nutrition that chickens get is passed on in the eggs, and barnyard chickens are likelier to get a healthier diet.