In study, TAVR is superior to surgery for low-risk patients with aortic valve stenosis. A large clinical trial has found that a minimally invasive procedure to replace a narrowed heart valve performed better than surgery in patients who were good candidates for surgery. Source 1k.
Surgery in general is always a risky process for all involved, especially when it involves the heart. Obviously TAVR isn't perfect but at least it posed a significant improvement since it greatly decreases the amount of deaths on those involved with this.