In my opinion, Avifauna is a "much" better park in all respects. Bigger collection, it usually has a very good flight show three times a day (in which they swap with species, so it's quite good to see two or even all three of them) and overall gives you a good feeling of a zoo day out. They have some relatively rare species (a hummer, coleto and kiwi among them) and a very nice lorikeet-landing (with feeding cups).
NOP is a bit old, tired, has sections with repetitive species and overall has a much shabbier look and feel to it then Avifauna. It also took me far less time to get through. But NOP offers two rare opportunities. First of all, it's on the brink of disappearing. As far as I understand it's already running on borrowed time as they seem to have lost their license to keep animals seized by customs and therefore a lot of their income. The plans to move in with "Dierenrijk" also seem to have bounced, so get there before it's gone.
Second: it also has some species that you will not find (almost) anywhere in Europe. Their Tropijoy rainforest building isn't all that big but gives you a chance to walk with some of Europe's rarest captive birds. For that, for me it felt like a "once in a lifetime" opportunity to walk in between a long-wattled umbrellabird, some calfbirds, purple-throated fruitcrows, spangled cotinga's, carmine bee-eaters and a few more utter rareties. Dotted among the park are a few more major rarities as well, like the only papuan cassowary on show in Europe. For me, it felt "special" to be able to see them, even if most of the park was as shabby as it was when we visited.
So if you're with a family on a day out, Avifauna hands down with it's hand behind it's back. Utter geek-factor, NOP inches nose first to Avifauna in my opinion...