The rubber bumper changes the harmonics of a cue, which coincides with the way the cue feels. The cue will vibrate upon impact, and your grip hand feels the vibrations. A very well balanced cue with high quality materials & top notch construction will resonate nicely, which means the vibrations run back & forth & back & forth & so on. It can also be heard as a "ping", "pong", "thud", etc. depending on the way the cue vibrates. Too much vibration & the cue will be uncomfortable. Too little vibration & it will feel dead. A rubber bumper was introduced to reduce noise. Brunswick actually called them "noise supressors" instead of bumpers. Depending on the size, hardness, mounting technique & quality of mount, the bumper may not interfere much at all or it can severely undermine & nullify the resonance of the cue.
Not much attention has been given to bumpers, but they are indeed a critical component, not a buttcap protector as most think. Yes, your cue certainly may feel much different without a bumper. Limb-savers are on one end of the spectrum with complete vibration dampening, and a hoppe butt with no bumper is on the other end with complete flow of vibrations. Everything else falls inbetween. I won't go into what's best because it's personal preference. But it is indeed another sub-science to be mastered if one is to master building players cues.
