The answer is: don't.
Comparing strings always works in string order:
1
10
11
...
2
20
21
...
Which is generally pretty useless for any practical purpose.
Instead, store your dates as Date or DateTime fields - that way you can compare them directly, enter only valid values, and return them as dates to your external code for formatting as the user wants: you don't need to look at it each time and compare what it might be against the users currently preferred display settings.