It seems that your char's hunger and thirst are seperate for each server.
If I am on east, eat till i'm bloated, then go back to west, I might be hungry, if i eat there, time passes and I get hungry again, then go back to east, I'll be full since I had eaten a lot last time I was on east. When I go back to west I will be hungry again.
I haven't tested this since the last update, so this may be old news.