Coilovers have a much higher spring rate than stock, they also have a higher spring rate than H&R's I believe. So the ride is going to be firmer, there's no way around that. The only ride advantage of coilovers is that the damping is adjustable. We all complain about the OEM ride mostly because it is way underdamped which leads to the bouncing, floating, "harshness" that people complain about. When I had OEM springs, the ride always felt unsettled. It was soft, but then over rough roads, it would feel a little uncontrolled with lots of bouncing. Swapping to H&R's helped with the floating feeling as the spring rate was higher so it controlled movement a little better at the expense of rougher ride over small.
Coilovers have a higher spring rate but also higher damping so it "should" be better matched. The ride is going to be worse over small bumps but over big dips I personally think it handles better as there isn't the floating feeling you get from OEM. I have BCs and I've run the original spring rates and currently have higher rate BC springs installed. Anyone who tells you that it rides better than OEM in all instances is lying, it can't. It's just that the damping is better matched to the springs so overall it handles better and rides better in some instances.
If they made better shocks and you could match them to your OEM springs, it would probably ride better than coils. FWIW, coilovers aren't designed for optimum handling on our cars or really any cars. They're designed to fit your car using off the shelf parts. The only custom part of the coilover is the shock mounts and top hats. The important stuff is standard, they just pick a spring rate that's close enough and the shock has enough adjustment to work. The coilover options we have aren't at the price points where they would do specific valving for our cars.