The JFBCContent plugin will insert the Comments and Like widgets surrounded by divs with id's of jfbccomments or jfbclike. On the menu item for the home page article, in the "System Parameters", you can specify a Page Class Suffix. For example, try using "-homepage". This will add a div like around your article. With these two classes, you can add something like the following to your CSS file to hide either of the Like or Comment boxes:
.contentpaneopen-homepage #jfbccomments, .contentpaneopen-homepage #jfbclike {
display:none;
}
Hope this helps, but if you need more info, just let us know!