If you're going to use only the US-ASCII (or ISO 646) subset of UTF-8, then there's no real advantage to one or the other; in fact, everything is encoded identically.
If you're going to go beyond the US-ASCII character set, and use (for example) characters with accents, umlauts, etc., that are used in typical western European languages, then there's a difference -- most of these can still be encoded with a single byte in ISO 8859, but will require two or more bytes when encoded in UTF-8. There are also, of course, disadvantages: ISO 8859 requires that you use some out of band means to specify the encoding being used, and it only supports one of these languages at a time. For example, you can encode all the characters of the Cyrillic (Russian, Belorussian, etc.) alphabet using only one byte apiece, but if you need/want to mix those with French or Spanish characters (other than those in the US-ASCII/ISO 646 subset) you're pretty much out of luck -- you have to completely change character sets to do that.
ISO 8859 is really only useful for European alphabets. To support most of the alphabets used in most Chinese, Japanese, Korean, Arabian, etc., alphabets, you have to use some completely different encoding. Some of these (E.g., Shift JIS for Japanese) are an absolute pain to deal with. If there's any chance you'll ever want to support them, I'd consider it worthwhile to use Unicode just in case.