Nvidia spends a lot more on driver support as a corporation, so the odds and historical reputation would support them having the more stable drivers. An interesting exercise is to read the driver discussions on Guru3d.com from each company's latest release to see if you can detect a difference in attitude from actual users.
http://forums.guru3d.com/showthread.php?t=392402
http://forums.guru3d.com/showthread.php?t=391474
This review of drivers from HardOCP presents evidence that Nvidia is better at support for new games, while AMD tends to lack and take as much as a half year before their drivers catch up.
http://www.hardocp.com/article/2013/03/04/2012_amd_nvidia_driver_performance_summary_review/#.VBYN0JUtCUk
Quotes from the Conclusion:
"In 2012 AMD had a rough time developing performance drivers and making them available to the public in a reasonable amount of time. It was evident that AMD was having problems during the first few months of the year."
"If there is one thing that stood out to me about NVIDIA's 2012 driver performances, it is how consistent the performances were. In most of our gameplay tests, NVIDIA's initial driver tended to have all of the possible performance boosts built in to it."
"It is also very important to have public drivers when your hardware is launched. We are looking at you AMD! It was clear that there was a lot of potential for performance in the Radeon HD 7970 and 7950, but we didn't see that performance realized until the middle of the year at least."
"If we could suggest one thing for each company to work on in 2013, it would be improve the driver performance earlier on. AMD needs to keep its drivers up to date and ready for new games during the entire year. It cannot slack off at some point, it is just not acceptable. NVIDIA should also try to improve its software in order to squeeze out extra performance in demanding and popular games. Having a steady and consistent framerate the entire year is good, but we would still rather have more performance if it is available."