The Advanced Tab will, for the most part, be an available feature within the General Tab of most Tiles. When clicking on the drop arrow symbol, you can see that there are features for configuring the stylistic nature of the tile. 

Within Advanced Styles, users can: 

When making changes via Advanced Styles within the General tab, it is important to consider some of the stylistic design approaches. Applying a drop-shadow when the rest of the tiles on your page do not have one will break consistency and may look less appealing to the eye. 

If a particular site within your site collection has a rounded theme, it would be in your best interest to maintain the consistency of that theme. Corners can be rounded at different magnitudes (measured in pixels). 

A Drop Shadow is a stylistic feature. In some cases, it is used to attract the eye or even to create a smooth transition between elements and the background image of your site. Apart from stylistic preferences and best practices, it is important to maintain consistency throughout the site in order to maximize consistency for visual reasons and for a smooth user interface.