I'd recommend the use of Number(), period. Unless you absolutely need to allow junk characters along with the numerals you're attempting to convert or, specifically to parseInt(), need to convert from a non-decimal base, there is very little reason to prefer either parseInt() or parseFloat() over Number().
Beyond that, parseInt() has some gotchas which can bite you.
- In some very ancient browsers, the default base is not 10. The traditional remedy for that bit of inanity is to always specify the base of the incoming numerals (usually base 10). e.g. parseInt('22', 10).
- In all older browsers, it will treat a leading 0 as signifying that the numerals are base 8 (octal). e.g. parseInt('010') would yield 8, rather than 10.
In summary: Unless you know for a fact that you'll need the unique features of parseInt()/parseFloat(), it's best to simply use Number().