Use the .date method:
In [11]: t = pd.Timestamp('2013-12-25 00:00:00')
In [12]: t.date()
Out[12]: datetime.date(2013, 12, 25)
In [13]: t.date() == datetime.date(2013, 12, 25)
Out[13]: True
To compare against a DatetimeIndex (i.e. an array of Timestamps), you'll want to do it the other way around:
In [21]: pd.Timestamp(datetime.date(2013, 12, 25))
Out[21]: Timestamp('2013-12-25 00:00:00')
In [22]: ts = pd.DatetimeIndex([t])
In [23]: ts == pd.Timestamp(datetime.date(2013, 12, 25))
Out[23]: array([ True], dtype=bool)