If you parse the JSON with eval, you're allowing the string being parsed to contain absolutely anything, so instead of just being a set of data, you could find yourself executing function calls, or whatever.
Also, JSON's parse accepts an aditional parameter, reviver, that lets you specify how to deal with certain values, such as datetimes (more info and example in the inline documentation here)
You are more vulnerable to attacks if using eval: JSON is a subset of Javascript and json.parse just parses JSON whereas eval would leave the door open to all JS expressions.
Not all browsers have native JSON support so there will be times where you need to use eval() to the JSON string. Use JSON parser from http://json.org as that handles everything a lot easier for you.
Eval() is an evil but against some browsers its a necessary evil but where you can avoid it, do so!!!!!
// In the third stage we use the eval function to compile the text into a
// JavaScript structure. The '{' operator is subject to a syntactic ambiguity
// in JavaScript: it can begin a block or an object literal. We wrap the text
// in parens to eliminate the ambiguity.
j = eval('(' + text + ')');
The advantage of JSON.parse is that it verifies the argument is correct JSON syntax.