It really depends on the live wallpaper. The ones that are very graphics or animation intensive will generally use more battery than the lighter ones. As a rule of thumb, the larger the filesize of the live wallpaper app, the more battery it is likely to use.
You should also check if the live wallpaper has any permissions. If it has network permissions, it may be checking the internet intermittently for a license check (if it's a purchased wallpaper, as opposed to a free one), or for ads for its settings screens. Checking the internet could potentially lead to additional battery usage.