TSX Cman,
There are so many coilover kits set up for various purposes that it is impossible to compare "a" coilover set up to the A-spec package. But, generally speaking, coilovers will be firmer, have less body roll, less dive and squat under braking and acceleration, and have the ability to at least adjust height, but at the cost of some loss in ride quality. By virtue of greater lowering, a coilover equipped car will look much sportier than an A-spec equipped car.
A-spec will provide near stock ride quality, very modest lowering, and improved handling.
There are those who will complain that coilovers are too stiff and many who feel that they provide a good balance of ride vs. handling. With the A-spec, I doubt you will find ANYONE who would complain that they are too stiff.
You maintain your full factory warranty if your A-spec is installed by the dealer.
Installing coilovers may result in portions of your warranty directly affected by the suspension to not be covered. I think this is a very minor issue as it is unlikely that a coilover suspension would cause any damage to your car unless you excessively lower your it or make an installation error.