Sometimes slicing can make download time faster, but sometimes slower depending on the use and situation. Browsers differ greatly in how they display large images during download, or the speed at which they read nested tables. Sliced images in certain instances can increase download time. Why slice?
Tables may not work in all browsers
Reading "CSS The Definitive Guide" by Eric A Meyer about table layout basically defined the table as individual layers. The table, columns groups, columns, row groups,rows and cells. Producing a web page layout with tables is complex, difficult to set up and cumbersome to update. Tables can be very slow to appear. Browsers must calculate the width and height of the table before it can begin to display the cell. If an image or slice is placed in a table the rate that the slice appears will be very slow.