You can compare date components:
NSDateComponents *otherDay = [[NSCalendar currentCalendar] components:NSYearCalendarUnit|NSMonthCalendarUnit|NSDayCalendarUnit fromDate:aDate];
NSDateComponents *today = [[NSCalendar currentCalendar] components:NSYearCalendarUnit|NSMonthCalendarUnit|NSDayCalendarUnit fromDate:[NSDate date]];
if([today day] == [otherDay day] &&
[today month] == [otherDay month] &&
[today year] == [otherDay year]) {
//do stuff
}
Edit:
I like stefan's method more, I think it makes for a cleaner and more understandable if statement:
NSCalendar *cal = [NSCalendar currentCalendar];
NSDateComponents *components = [cal components:(NSYearCalendarUnit|NSMonthCalendarUnit|NSDayCalendarUnit) fromDate:[NSDate date]];
NSDate *today = [cal dateFromComponents:components];
components = [cal components:(NSYearCalendarUnit|NSMonthCalendarUnit|NSDayCalendarUnit) fromDate:aDate];
NSDate *otherDate = [cal dateFromComponents:components];
if([today isEqualToDate:otherDate]) {
//do stuff
}