Well, they do have somewhat different meanings.
Ĝisdatigi means to make it so that it is relevant to the current date. For example, the Vikipedio page about lernu.net mentions things like "Zamaĉo" and the chat room, that have not been around in quite some time, as if they were still there, and says nothing about the current features. Thus, it is definitely ĝisdatigenda. I would also use it in the sense of "update someone about something", because you are bringing their understanding of the situation to match up with how it stands now.
Aktualigi is similar, it means to make current. So, if I maintain a list of Esperanto events, I need to aktualigi it regularly for it to be any use. But using aktualigi in the sense of "update someone about something" sounds weird to me; I'm not totally sure why.
Novigi means to make new. So, I would describe the new lernu.net as novigita, and if I remodeled my house, I would describe it the same way, but I would not say it is aktualigita or ĝisdatigita. If I described the Vikipedio page or the list of events as novigita, to me that implies that I reconstructed the whole thing, so that now it is for all practical purposes nova, just with the same web address.