Given the high level of statistical certainty that particle physicists strive for from experimental data, how much of a difference does the approach matter by the point where they are confident enough to endorse the theory?
For instance, if you are going for five sigma (like in the Higgs Boson discovery), how would the different techniques change when the data is considered sufficient, if at all?
The five-sigma threshold is a limit for making big public announcements, or claiming definitive discrete discoveries (like new particles) that non-particle physicists can take for granted. But there's lots of intermediate work done at accelerators that can't reach that threshold but still informs further work, and even influences the construction and design of the next multi-billion dollar machines. The bi-annual Review of Particle Physics is as thick as a phone book and filled with (usually) 95%-confidence intervals for measured values. For instance, here is the 89-page summary of what is known about the tau particle:
For instance, if you are going for five sigma (like in the Higgs Boson discovery), how would the different techniques change when the data is considered sufficient, if at all?