As in most things with particle physics, it's a combination of both. Theory predicts a wide band and then experimentalists come in with the best estimate they can make. Some theories are excluded and other are refined. There are another round of predictions and when the experiments get powerful enough, they can challenge or support some predictions.
Some of the best data for branching ratios comes from e+e- (electon-positron) colliders such as LEP (literally, the Large Electron-Positron collider). In these colliders, we can fine-tune the energy to produce massive amounts of particles we care about. From that, we can see how they decay. Mostly, Upsilons decay into massive sprays of hadrons and leptons (called jets in particle physics). These can come from decaying Tau particles (the much much heavier cousins of muons and electons) or from quarks/hadrons decaying over and over and over again into things like Kaons, pions, muons, electrons, photons, and other lightish particles. In the relatively clean environment of a e+e- collider, we can reconstruct these jets and determine which may have come from Upsilons. Combining this with a whole bunch of other measurements (and some theory) lets us determine the branching ratio (how often a particle decays into certain things).
Some of the best data for branching ratios comes from e+e- (electon-positron) colliders such as LEP (literally, the Large Electron-Positron collider). In these colliders, we can fine-tune the energy to produce massive amounts of particles we care about. From that, we can see how they decay. Mostly, Upsilons decay into massive sprays of hadrons and leptons (called jets in particle physics). These can come from decaying Tau particles (the much much heavier cousins of muons and electons) or from quarks/hadrons decaying over and over and over again into things like Kaons, pions, muons, electrons, photons, and other lightish particles. In the relatively clean environment of a e+e- collider, we can reconstruct these jets and determine which may have come from Upsilons. Combining this with a whole bunch of other measurements (and some theory) lets us determine the branching ratio (how often a particle decays into certain things).