We compare it with homological equivalence and smash-equivalence for cobordism cycles. For the former, we show that homological equivalence on algebraic cobordism is strictly finer than numerical equivalence, answering negatively the integral cobordism analogue of the standard conjecture (D). For the latter, using Kimura finiteness on cobordism motives, we partially resolve the cobordism analogue of a conjecture by Voevodsky on rational smash-equivalence and numerical equivalence.