Suspension is one of the more 'mythical' parts of car tuning to most. Yet in reality its not so complicated once you get your head round the understanding of it all (and sometimes it seems to defy logic!)
To the chap above the wanted to know the spring poundage of his car - bring the car in to us - we'll pop a damper/spring off and test them for you - you'd be amazed at the variation you'll find in a 'fixed' spring - road car springs are as you might suspect not always the greatest quality and you'll find a degree of variance between springs, side to side and corner to corner. 
In short are coilovers better than a spring and damper combination - yes. But they are equally often an unnecessary over kill on a road car as you are simply not using the car to the extent that you gain the maximum benefit from the upgrade. Coilovers feel different for a number of reasons - most likely is that your coilover kit, just as your uprated spring and damper kit will, has increased spring poundages - effectively the force required to compress the spring. Increased spring poundages can lead to a 'crashy' ride, but the spring is their to control the damper underneath it - effectively the spring acts as a measure against the damper. Most road cars are fitted with 'progressive' springs - as are most uprated damper kits - these might be familiar to you as you'll see the spring will tighten up and the coils get closer as the spring moves to one end. The effect of this is the the spring poundage is not consistent - it gets harder as the spring is compressed meaning it soaks up the small bumps but trys to hold the car firmly when cornering hard. A coilover (not always but majoritively) is fitted with a constant spring - particularly when they are increased poundage this can leave a ride feeling harsh and non compliant over bumps. But on a circuit or a road when driving hard a constant spring gives you more control over the car and restricts roll and weight transfer. 
Generally but not always coilover will be damping adjustable, just as your uprated kit might be. Damping adjustment is generally '2 way' this means 'Bump' and 'Rebound'. Simply put, bump adjustment controls the valving of the damper during compression meaning the speed the damper adjusts to impacts or compression from cornering. Rebound is the speed the damper returns from that impact or compression. Many road coilovers a 'ratio' adjustable - meaning that bump and rebound are adjustable in a fixed ratio of say 2:1. Thus if you soften the damping 2 clicks it adjusts the bump by half the amount of the rebound. I won't go into the effects of bump and rebound because I'll be here all night and I want to go home! But if you're interested there is some good stuff on the net about it. 
Lastly, and the main difference, a coilover is height adjustable - meaning you can control ride height (for those that want to 'slam' their cars usually the most important bit!), rake and corner weights. Rake is the front to rear stance - i.e. nose down or arse down! It moves the centre of gavity around in the car and can make a significant impact on the handling characteristic - including promoting under steer or over steer. Ride height - the theory says a low centre of gravity is good so wind those coilies down - however on many VAG platforms this effects the 'roll centre' of the car. Additionally you also shorten the damper travel and place more reliance on the spring - not always a good thing and part of the reason that so many really decked cars feel so damn awful to drive on the road! A coilover kit also allows corner weight adjustment. Not often in a car is everything distributed equally (its got the driver on one side to start with!) and thus the weight applied to each wheel is not often equal - balancing this weight can significantly improve the characteristics of the car. Ideally in a FWD car you want to balance the car accross the front (those with the largest weight) and get the rears as close as possible. Its not usually possible to balance all 4 wheels perfectly but you can get it pretty close. Corner weights are adjusted through ride height and work on the theory that each and every force has and equal and opposite force - thus on occasions defying logic by increasing the weight on that corner by increasing the ride height of the corner (a spring under greater compression exerts more force onto the road). 
Tracking also plays a major part - the 'toe' angles of the car (the angle in and out of the front of the wheels from the parallel) as does camber (the vertical angle in and out from parallel). These factors can be adjusted regardless of your suspension set up and you could find some big changes. 
So yes - I believe that a coilover is a better set up - but how many are really going to test them on a road - not many probably 
