Anti-aromatic or Non-aromatic
Whenever you want a definition of a chemical concept, you should refer to the IUPAC's Gold Book which in this case states that antiaromatic compounds are 


  compounds that contain  4 n(n ≠ 0) π-electrons in a cyclic planar, or nearly planar, system of alternating single and double bonds, e.g. cyclobuta-1,3-diene.


A corollary to this rule is that all the atoms must have an sp2-hybridization, so the orbitals can overlap. However, the carbon bearing the negative charge has an sp3-hybridization, i.e. they does not count as π-electrons but σ-electrons and that breaks the rule of alternating single and double bonds. So both anions are non-aromatic.

Edited after the OP opened my eyes on a big mistake I had made in answering his question. Sorry about that.