I am not entirely sure it is a fair comparison - I would hope the Nat Geo clip seems childish, as the author says, because it is in fact a children's programme, while the BBC one is for a general public. I actually watched many Attenborough documentaries with my daughter when she was younger, and there were often tears involved, what with the cruelty of nature and such. (Attenborough, by the way, must rank as one of the greatest contemporary Britains...)
Especially when you bear in mind that natural history presentation is only one of the strings to his bow. He was Controller or BBC2 and was tipped to be Director General of the BBC except that he decided that he couldn't stand working behind a desk for much longer.