Both will be -ABOUT- the same viscosity when at operating temperatures, but as the temperature of the oil drops, the 5W-30 will generally thicken more than the 0W-30 will. The difference generally gets more dramatic as temperatures fall toward freezing and below.
In my opinion, there is absolutely no detriment to using a 0W-30 where a 5W-30 is specified, and in fact, I'm becoming of the opinion that 0W- oils are beneficial to everyone, including those who live in hot climates. Even a 100*F cold start is "cold" for motor oil, and the 0W-30 will generally flow faster than a 5W-30 will...even at 100*F.
I use the word "generally" a lot. That is because these numbers are viscosity grades, with allowable ranges associated with them. So sometimes you can have an oil that's on the "thick" end of a range and an oil that's on the "thin" end of a range and still have the same grade printed on the bottle. It's totally possible that the 0W-30 might be thicker than the 5W-30 at operating temperature...but both would still be in the range allowed to be labeled "30".