Both are correct. According to my unscientific test, "Changes are needed" is more popular with 46.7 million hits, while "Changes are necessary" has 34.5 million hits.

They are both correct depending on the context. Needs are often contrasted with wants. People need food, water, and shelter, but they want burgers, Mountain Dew and reddit.com. Necessary is the same as required. I have a software business with 5 products. One of the products must be changed in order keep selling it. The business can survive on 4 products. Changes to the software are necessary to keep selling it, but changes are NOT needed for the business to survive. If the business can't survive on 4 products then changes ARE needed and necessary.

Like Timo said, both are correct. The difference is quite minor. "Changes are needed" makes it seem like you need to make changes to something at the given moment before anything else proceeds e.g. "changes to the plan are needed for the new building" -> implies that we need to make change before we do anything else for the new building "Changes are necessary" implies that some kind of change is very important or significantly useful but not necessarily urgent/first priority e.g. "changes to the plan are necessary for the new building" -> implies that some change should occur to the plan before the building is finished/finalised