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The short (albeit not very interesting) answer is that E as a symbolic expression (first case), has a very different factor method than E as a polynomial (second case).

For example, consider:

sage: var('y t'); E = -2/3*y + 2/3 * t; type(E)
(y, t)
<type 'sage.symbolic.expression.Expression'>

Type one question mark to get the help (docstring), or two question marks to see what happens "under the hood" (read the code just after the docstring):

sage: E.factor()
2/3*t - 2/3*y
sage: E.factor??
Source:
    def factor(self, dontfactor=[]):
        """
        Factor the expression, containing any number of variables or functions, into
        factors irreducible over the integers.
...
from sage.calculus.calculus import symbolic_expression_from_maxima_string, symbolic_expression_from_string
....

So factor here dispatches a suitable function from the Maxima interface.

Now, let's cast that symbolic expression into a polynomial

sage: P = E.polynomial(QQ); type(P)
<type 'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular'>  
sage: P.factor()
(2/3) * (t - y)
sage: P.factor??
Source:
    def factor(self, proof=True):
        """
        Return the factorization of this polynomial.
...
cdef ring *_ring = self._parent_ring
....
cdef MPolynomialRing_libsingular parent = self._parent
....
.... return Factorization(list(U) + FF, unit=U.unit())

so if i get it right, in this case Sage makes use of the Factorization function of the CAS for polynomial computations Singular.