As we would say 'back in the olden days' the nappy bag I had was small and I used it for both DD. I had cloth nappies, cover, wipes, nappy cream, a change of clothes and odds and ends and it was plenty big enough.
It depends if its the only bag you want to take with you. I always had my handbag as well.
I myself never liked a big bag but some people do, its really a personal preference.