Both work, but for expressing different meanings.
"One of the big issues" means you have many big issues and you are discussing one of them.
"One of the biggest issues" has a comparative element: the issue is among the biggest, and there are smaller, less important ones.
"Biggest" is a superlative adjective. Superlative adjectives express a comparative relationship between AT LEAST THREE things and points to the ONE with the greatest intensity or degree of a certain quality. So it seems wrong to write "one of the biggest issues" when there should be only ONE BIGGEST issue. This is where you are looking at an idiomatic expression. "One of the (superlative adjective)" is commonly used to emphasise the great intensity of a quality in something while acknowledging that such an intensity can also be found somewhere else. Example: "One of the greatest writers of his time." This person is among the best writers.