TDateTime appDateFromVector = TimeOf(appointmentsForFind[i].getAppDateTime());
DateTime appDateFromControl = TimeOf(DateTimePickerAppointmentTime->Time);

if (appDateFromVector == appDateFromControl)

TDateTime TimeA, TimeB;

// offset TimeB by one hour
TimeA = Now();
TimeB = IncHour(TimeA, 1);

// use CompareTime function
if (CompareTime(TimeA, TimeB) == EqualsValue)
{
  ShowMessage("Both times are equal.");
}

// use SameTime funtion
if (SameTime(TimeA, TimeB))
{
  ShowMessage("Both times are equal.");
}