Beauty is in the eye of the beholder. The "best" TV pictures and sound are those delivered by whichever television service provider you ask. That is the normal way of the world and perfectly understandable. The question of fiber optic TV or cable service delivering the best quality often generates two answers: both of them "yes."
Cable television service companies will tell you that their digital service is just as clear, crisp, and clean as delivered by fiber optic TV. Their coaxial cables are high speed, high volume, proven methods of getting you high quality TV programming for years. All of this is true and in most areas, cable high speed Internet, digital phone, and television service is first rate.
Fiber optic systems (AT&T U-verse and Verizon FiOS, for example) have necessitated the installation of miles and miles of state-of-the-art fiber optic cables to form the delivery system for its modern computer servers. They now deliver SD and HD television service, very high speed Internet, and digital phone service to an ever-expanding customer base. Neither Verizon FiOS nor AT&T U-verse is "everywhere" yet for a number of reasons. They are replacing thousands of miles of standard shielded (protected) copper wires with fiber optic cable and it takes some time. Also, there are still many areas of the U.S. that have franchise agreements with cable television service that prohibits any similar competition.
In these cases, fiber optic must wait for franchise renewal dates and ask the local authorities to allow them to offer their service. To date, they are becoming more successful in their efforts and their television service is now offered in many markets that are already pleased with their broadband Internet and digital phone service.
The question of who is "better" remains, however. The choice is really dependent on your personal preference. Both deliver wonderful TV quality. You should probably select the provider you "like" best. Consider pricing as a major issue. Since both give you great TV -- as does satellite TV (DirecTV and DISH Network) -- you shouldn't suffer quality problems. But if you can get a bundled (packaged) special deal from one or another for lower monthly cost, you should consider the benefit to you.