Anda tidak perlu menerapkan to_date() ke sysdate . Sudah ada:
select 1
from dual
WHERE sysdate BETWEEN TO_DATE('28/02/2014', 'DD/MM/YYYY') AND TO_DATE('20/06/2014', 'DD/MM/YYYY');
Jika Anda khawatir tentang komponen waktu pada tanggal, gunakan trunc() :
select 1
from dual
WHERE trunc(sysdate) BETWEEN TO_DATE('28/02/2014', 'DD/MM/YYYY') AND
TO_DATE('20/06/2014', 'DD/MM/YYYY');