It is not clear from the question if you're referring to the strips being connected in series or in parallel. Each setup has its distinct advantages and resulting uses. For example, connecting layers in parallel will increase the equivalent area of the capacitor, thereby increasing its capacity.

According to http://en.wikipedia.org/wiki/Capacitor#Structure "For small values of capacitance (microfarads and less), ceramic disks use metallic coatings, with wire leads bonded to the coating. Larger values can be made by multiple stacks of plates and disks. Larger value capacitors usually use a metal foil or metal film layer deposited on the surface of a dielectric film to make the plates, and a dielectric film of impregnated paper or plastic – these are rolled up to save space."

According to http://en.wikipedia.org/wiki/Capacitor#Networks "Capacitors in a parallel configuration each have the same applied voltage. Their capacitances add up. Charge is apportioned among them by size... Connected in series, the schematic diagram reveals that the separation distance, not the plate area, adds up. The capacitors each store instantaneous charge build-up equal to that of every other capacitor in the series. The total voltage difference from end to end is apportioned to each capacitor according to the inverse of its capacitance. The entire series acts as a capacitor smaller than any of its components"

The same source continues, explaining the use of multiple layers connected in series to reduce the voltage across each layer of dielectric, allowing higher voltages to be used in the circuit across the capacitor without risking breakdown of the dielectric: "Capacitors are combined in series to achieve a higher working voltage, for example for smoothing a high voltage power supply. The voltage ratings, which are based on plate separation, add up. In such an application, several series connections may in turn be connected in parallel, forming a matrix. The goal is to maximize the energy storage utility of each capacitor without overloading it."

The bottom line is that using multiple layers and then rolling them up allows a smaller package which can provide higher capacitance if the layers are connected in parallel to each other (for low voltage applications), or providing higher voltage rating, at the expense of a reduced capacitance if connected in series (e.g. for smoothing out the output from a high voltage supply).

According to electricianeducation.com, it was posted that "Capacitors may be connected in series or in parallel to obtain a resultant value that may be either the sum of the individual values (in parallel) or a value less than that of the smallest capacitance (in series). Connecting capacitors in parallel effectively increases plater area and thereby increases total capacitance."