There isn't a simple answer to this question. Both types of surgery are being used today. Big changes have occurred in how both operations are done. Short- and long-term results are being studied.
Fusion is meant to stop all motion in the spine at the level of the fusion. It doesn't really change the original problem. For example if a fusion was needed because there's degeneration, fusion only masks the true disease process. It doesn't get rid of the original problem.
Fusion works best when motion is causing the pain. The segment gets fused and can no longer move so the pain is gone. Fusion can cause increased motion at the level above or below the fused site. This may increase damage faster and sooner at those levels.
Disc replacement corrects the abnormal motion. The space between the vertebra is kept open. The patient gets pain relief and return of function. Problems can occur if the artificial disc isn't put in place just right. The disc can also crack or break. They don't last forever and may only hold up 10 to 20 years.
Studies comparing fusion to implants have mixed results. The best patient for a disc replacement seems to be someone with only problems at one level in the low back area. The doctor must have good training and experience to get the best results.