Well the title is a little bit of a lie. One is new, the other is only new-ish.
The first trailer is the new trailer of NieR Replicant which is currently Japanese only PlayStation 3 exclusive. The other trailer is of NieR Gestalt (known simply as Nier for North America and Europe) is a Xbox 360 exclusive in Japan, but in North America and Europe it is on both PlayStation 3 and Xbox 360. Yeah, it is a little confusing.
Both games are being touted as separate experiences in Japan, but the amount of change in each title has yet to be seen.
NieR Gestalt, or rather the one we are getting, is currently planned for a world wide release of April 23rd for both the Xbox 360 and PlayStation 3 in North America and Europe.