You could use a combination of sprintf and strcmp to achieve your described behaviour e.g. similar to this
// date and time from RTC
DateTime now = rtc.now();
// date and time to compare with - this is provided by you
String datetimeCompare = "1970/01/01 00:00:00";
// this buffer must be big enough for your complete datetime (depending on the format)
char datetimeBuffer[20] = "";
// convert current date and time to your specific format
sprintf(datetimeBuffer, "%04d/%02d/%02d %02d:%02d:%02d", now.year(), now.month(), now.day(), now.hour(), now.minute(), now.second());
// perform the comparison
if(strcmp(datetimeBuffer, datetimeCompare.c_str()) == 0)
{
// datetime strings are the same
}
Or you convert your rtc.now() DateTime according to your format as described over at the arduino stackexchange.