The one with the highest likelihood is the one with the best chance of producing your data --- as long as the likelihoods can be compared.
At the very least, this requires that no constants have been left out (you can normally leave out constants because you normally compare things with the same constants), and that they all have the same number of parameters (which the usual distributions by these names will do).
Indeed, you could take a Bayesian point of view and compute relative probabilities under some prior, like a uniform (though I don't know that I'd use a uniform prior across those models; it would be a very very rare situation where I'd equally seriously entertain all of those).
i.e. "Conditional on only between these distributions, the relative probability is mostly on gamma (82%) or Weibull (18%)" ... but many people seem to deny that such a comparison can be validly made.