Try foating the content of the TD tags instead of the tags themselves.
It makes no sense to float TD tags as their position is predefined by their place within the table. One of the browsers is therefore correctly ignoring the nonsense floats while the other is incorrectly rearranging the table.
Try removing those float styles from the TDs. There’s no need to float table cells. They sit side by side anyway. If you want to float the contents, apply the float directly to them.