I don't know about "most successful," but Ariane 5 flew 83 consecutive missions without a failure, and had a 95.7% success rate overall. It was used to launch the James Webb Space Telescope.
> The Ariane 5 program also selected the best components for Webb based upon pre-flight testing. For example, for the Webb-designated rocket, the program used a main engine that had been especially precise during testing. "It was one of the best Vulcain engines that we've ever built," Albat said. "It has very precise performance. It would have been criminal not to do it."
From https://arstechnica.com/science/2022/01/all-hail-the-ariane-...
> The launch was described by NASA as "flawless" and "perfect".[4] A NASA systems engineer said “the efficiency or the accuracy with which Ariane put us on orbit and our accuracy and effectiveness in implementing our mid-course corrections” meant that there is “quite a bit of fuel margin ... roughly speaking, it’s around 20 years of propellant.”[16][17]
From https://en.m.wikipedia.org/wiki/Ariane_flight_VA256
When you have many satellites and want it cheap, go with SpaceX. If you have one priceless irreplaceable satellite hundreds of people spent decades building, go with Ariane. There is market for both.
Had NASA paid for the launch, both the Delta 4 (Heavy) and the Atlas 5 has the necessary NASA certification.