the civic is a more stiffly sprung car so it won't ride quite as well but it will handle and corner with more control and generally feel more 'sporty'
however there's some checks you can do to ensure that the car is riding as well as it can
The first thing to do is check that the tyre pressures are correct to those stated in the manual / on the door jamb sticker, if this is OK then its also worth making sure that the suspension geometry is correct as if a camber or rear toe setting is out then this would make the car feel nervous,
If looks Ok then I'd consider fitting a taller profile tyre with a smaller diameter wheel, this will add some compliance to the ride and generally calm the quick responses. An alternative is to keep the current wheel and replace the tyres with some of a softer sidewall so removing some of the compliance in the system - Toyo's for example
This is especially true if you have run-flat tyres currently fitted
If you look on the tyre at the end of the number eris there's a letter the number just before this letter denotes the load capacity and therefore sidewall stiffness.
ie 225/55 R16 91V its the 91 you're interested in try a tyre with a lower figure and you'll get a softer tyre, however bear in mind this will also soften the steering response
Its also worth checking that all the main suspension pivot points have been tightened with the car on its wheels not in the air as this can add a lot of friction to the suspension and lastly check that the brakes aren't binding at all as this too can make the ride very jerky and bouncy