Can you identify the hardest-to-get weapons in your game? How about the tiers of armor for your class? Can you tell how far someone is into the endgame based on what s/he is wearing? This is the standard item-based model of character (appearance) customization. There may be options to make your orc 5% bulkier or give your elf fourteen shades of blue or green eyes, but it will be covered by equipment anyway. Making yourself look interesting is almost always a result of making yourself powerful, and your appearance suggests your capabilities. The guys in those robes heal, and the guys in those robes blow things up, and the guy in that hat is obviously very experienced. Looking good is a reward worth working for, and it immediately commands the appropriate respect from the knowledgeable (and often wonder from the ignorant).
Or is form radically separate from function? City of Heroes gives you almost all the costume items up front. Norrath and Middle Earth have cosmetic tabs for equipment to cover your mismatched raid gear (a half-measure to let you lock in your favorite achievement-based appearance). In a world where the same gesture might be a sword-slash or a fireball-toss, there is no need to connect how something looks to what it does. This allows the maximum of customization and individualization, and it can come as early as you like. I have seen swordfights somewhere between a feline hominid and a lightsaber-wielding lesbian mermaid slave; spectators included several librarians, someone in an oversized cowboy hat, and a robot-thing with a cow levitating over it. None of these had special abilities.
You can cross the two a bit. Item-based systems have dyes for customization, although the colors can still signify wealth levels. Function-free systems can have unlockable pieces or categories, like City of Heroes auras that are available after level 30, costume sets reserved for long-time subscribers, or weapons that require certain badges (and you can bet I show off my Rikti Axe).
Is one better, or is it a matter of taste? I often enjoy a connection between form and function, such as making the meaner monsters bigger. You can even reverse the two standards: have item-based play that does not affect appearance (like Diablo II sockets or City of Heroes enhancements) or non-item play that ties appearance options to accomplishments.
Yeah, I keep citing City of Heroes here. I have played a few years of it, and its costume designer is still the industry benchmark.