Learn Polish: Wolę uniwersalne ubrania, zwłaszcza dżinsy. - I prefer versatile clothes, especially jeans.

Yes, they are highly interchangeable here. However, zwłaszcza is often the most natural choice when you are singling out a specific example (jeans) from a broader category you just mentioned (clothes). Szczególnie can feel slightly more focused on the intensity of your preference, while przede wszystkim would mean you prefer jeans "above all else."

I thought uniwersalne meant "universal". Why is it translated as "versatile"?

While it can mean "universal" in an abstract sense (like a universal truth), when applied to physical objects, clothing, or tools, uniwersalny is the standard Polish word for "versatile" or "multipurpose." It implies that the item is practical and suitable for many different occasions.

Does the particle zwłaszcza affect the grammatical case of dżinsy?

No, focus particles like zwłaszcza do not govern cases. The noun dżinsy is still the direct object of the verb woleć (to prefer), which requires the accusative case. Because dżinsy is a non-masculine-personal plural noun, its accusative form happens to look identical to its nominative form.

Why is "jeans" spelled dżinsy here?