I visited both, on a whim, while I was by accident in the area, prodded by a comment just like this. It was a fantastic experice! And I did enjoy the National Museum of Computing more! There was an excellent elderly guide there that seemed to have been in computing since forever and told us stories of when he worked on machines just like the ones in the exhibition. A small bunch of us nerdy guys hung around him and it was great interacting with them and the tour guide. It was really really an excelent experice!

If I'm ever in the area again, I would love to revisit and I would love to have my young son with me as well.