The difference, as you pointed out stems from NULL date values when you create your IF statements. In each formula, you have only 1 decision rule:
in (a), you set anything WITH a date value < 6/1/12 to be 'existing', and all else as 'new'
in (b), you set anything WITH a date value >= 6/1/12 to be 'new' and all else as 'existing'
In both formulas, NULL values cannot be evaluated against the IF criteria, so the NULL values get assigned the "ELSE" value
If you wanted to force (a) or (b) to result in the same thing, you would need to add a 2nd decision rule to each:
IF [customer_startdate] < #6/1/2012# THEN 'existing'
ELSEIF [customer_startdate] >= #6/1/2012# THEN 'new'
Is this causing you a specific problem, or were you just curious? If you need more assistance, feel free to post a screenshot, packaged workbook, or just another specific question.
Thanks a lot, Mark! That was definitely helpful.