Placement of RF module for better performance
The main rule for such antennas is not to have any metal part near them, be it the board copper or not. Or, if this is impossible, to have them as far as possible. If you look at the area of the module around the antenna, you'll probably see that there is no copper in any of its layers.
Given that, and provided that you made a keepout area on all layers of your board under the antenna, the two choices that you presented are almost the same, with the one in which the module is up marginally better because it's a bit farther from the battery. But even then the result may have quite low performance, because you still have lots of metal areas near the antenna. No matter what is the chemistry of the battery, it'll most certainly be totally opaque to RF, so the better would be to "slide" the module to the left until the antenna is outside the board area and there's nothing below it.