Dextrose (corn sugar) is almost completely fermentable. That means corn sugar = alcohol and almost no flavor.
DME will provide fermentables and flavor. You will get less alcohol per volume from the dme, but you will also leave some malt character, which is pretty important for the beer.
Since you're using Coopers Hopped Canned LME (presumably), you may also want to add a little bit of hops too. It may help balance it. I'd recommend an ounce at 15 mins of boil left, which will add a little aroma, too. Ask your LHBS what kind of hops might complement the kit.
You could also just brew about 3 gallons with the hopped LME and get a real feel for the intended character w/out the "cidery" bite of the corn sugar mentioned above(it was noticeable to me and friends when I started).