Usually big drivers sound big, if that's what you are trying to get at.
The feel of big and small drivers is different. When you hear a big driver play, you know it's a big driver playing. Most reviewers use the phrase "sounds big" to describe the effortlessness and dynamics of the sound. Another meaning is the speaker sounds like it's using a larger driver in a larger cone.
Like Decadent Spectre above explained, with large drivers come an effortless presentation, due to it's inherent ability to move more air and subsequently generate higher SPL with greater dynamics. However, this comes for a price.
Managing drivers with large cone is not as easy as managing drivers with smaller cones. There are too many factors. Common laws of physics apply. For larger cones the driving motor, the voice coil need to be of much higher quality to control the movement of big heavy cones and the cone material itself needs to be much better quality to provide linear excursion for a distortion free sound.
Cabinet design for a large speaker driver is not as complex as for small drivers. You can suspend a large driver in an appropriate sized box and they can still generate good sound. Things are more complex for small driver cabinets. The number of drivers multiply quickly as designers attempt to simulate the large cone area of large drivers.With increased number of drivers, the cabinet design becomes complex, so does the cross-over design, as there are too many things to synchronize and manage. However, once a set small drivers are made to sing together in harmony, they can't be beat for many a parameters modern day audiophile crave about, most notably speed and imaging accuracy.
In the good old days some of the best sounding speakers were all designed around large drivers. But with advances in computer enabled modeling has enabled designers to try out permutations and combinations of drivers and cabinets without actually sweating it out on drivers and cabinets. No wonder in modern days, some of the best sounding speakers are all using small drivers.