I'd have to type in the date manually which is pita.

Separate fields formatted in ISO8601 format?

It all depends on your use case, dropdowns are a nightmare to get right as setting the dropdown for months influences the amount of options in the dropdown for days. Same goes for years.

If you're asking a user to input a birthdate it doesn't really make sense to show a date picker, as the actual day and week doesn't really matter, also, each and everyone of us have our birthdates memorized as a set of numbers, so offering separate input fields allows for quicker input.

I mostly test if <input type="date"/> is supported, if so, leave it alone (the device will show a date picker). Else, offer input fields based on the options described above.