Comparing with the non-collinear optical parametric amplification (NOPA), the gain bandwidth could be significantly enhanced by the wide-angle NOPA (WNOPA), i.e., with a divergent signal (WNOPA-S) or pump (WNOPA-P). In a uniaxial crystal, the spectral symmetry/asymmetry of WNOPA is introduced. In WNOPA-S, the ultra-broadband gain spectrum can be obtained in two phase-matching directions at both sides of the pump, however, the output is heavily angularly dispersed. In WNOPA-P, although the gain bandwidth enhancement is only achieved in one phase-matching direction, i.e., on the opposite side of the crystal axis, it is free of angular dispersion. The stabilities of the gain spectrum in NOPA and in WNOPA-P are experimentally compared and theoretically analyzed. Compared with NOPA, WNOPA-P supports an even broader and more stable gain spectrum, and compared with WNOPA-S, WNOPA-P is angular-dispersion-free. The conversation efficiency of WNOPA-P is the same as NOPA. We suppose WNOPA-P is ideally suitable for the amplification of stable ultra-broadband few-cycle pulse lasers.