If only scientists had proper stat courses...
Does the MCMC computing method allows one to write better papers? More likely to be considered? Or more precise, scientifically speaking?
There are two big benefits to using Bayesian statistics, of which MCMC-type methods are a component:
1. They allow you to incorporate prior knowledge. For well studied systems, that means your results and data are automatically put into the context of the field as a whole. That's...cool.
2. Bayesian estimates - especially Bayesian posterior intervals (the equivalent to the usual confidence interval) actually have the interpretation that people think confidence intervals have. Namely that there's a 95% probability that your estimate is in between the bounds.
Those are statistical reasons why a paper might be "better". It's also a good way to make an ordinary paper somewhat "sexier" which might get it into a better journal, though at times it spooks reviewers.