This is actually a harder problem than it appears because of the boundary cases where the variance that you don't care about crosses a threshold for a value you are checking. e.g. the millisecond difference is less than a second but the two timestamps cross the second threshold, or the minute threshold, or the hour threshold. This makes any DateFormat approach inherently error-prone.
Instead, I would suggest comparing the actual millisecond timestamps and provide a variance delta indicating what you consider an acceptable difference between the two date objects. An overly verbose example follows:
public static void assertDateSimilar(Date expected, Date actual, long allowableVariance)
{
long variance = Math.abs(allowableVariance);
long millis = expected.getTime();
long lowerBound = millis - allowableVariance;
long upperBound = millis + allowableVariance;
DateFormat df = DateFormat.getDateTimeInstance();
boolean within = lowerBound <= actual.getTime() && actual.getTime() <= upperBound;
assertTrue(MessageFormat.format("Expected {0} with variance of {1} but received {2}", df.format(expected), allowableVariance, df.format(actual)), within);
}