The two functions are really quite different.
parseInt() extracts a number from a string, e.g.
parseInt('1.5')
// => 1
Math.round() rounds the number to the nearest whole number:
Math.round('1.5')
// => 2
parseInt() can get its number by removing extra text, e.g.:
parseInt('12foo')
// => 12
However, Math.round will not:
Math.round('12foo')
// => NaN
You should probably use parseFloat and Math.round since you’re getting input from the user:
var number = parseFloat(prompt('Enter number:'));
var rounded = Math.round(number);