Drop down menus are often ugly on a Phone applications. They open up a new view state and you’re practically navigating away from the page you’re currently navigating. From a UX-perspective that’s bad. To use the dropdown well – you need to style it as the application so the user know that they are still in the same app.
Accordion menus are probably a better choice since you remain on the page you’re currently viewing, which lets the user know where they are at all times. If you have several sub-menus, only use one open at a time keeping the scrolling to a minimum. If you open a new accordion menu, close the other ones.
Remember that phone app users often turn of the screen at any given moment. If you do that on an open drop-down menu, the user (often) have no clue where they are and have to start over. But on an accordion menu, you know where you are.
-Android drop-down menu-