Both will be -ABOUT- the same viscosity when at operating temperatures, but as the temperature of the oil drops, the 5w30 will generally thicken more than the 0w30 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 0w30 where a 5w30 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 0w30 will generally flow faster than a 5w30 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 0w30 might be thicker than the 5w30 at operating temperature...but both would still be in the range allowed to be labeled "30".